Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor **Mathway**. Visit **Mathway** on the web. Download free on Google Play. Download free on iTunes. Find the **Inverse**. Write as an equation. Interchange the variables. Solve for . Tap for more steps... Rewrite the equation as . Set up the composite result **function** * g ( arctan ( x)) = tan ( arctan ( x)) g ( arctan ( x)) = tan ( arctan ( x)) The functions tangent and arctangent are inverses*. g ( arctan ( x)) = x g ( arctan ( x)) = x. Since g ( f ( x)) = x g ( f ( x)) = x, f − 1 ( x) = tan ( x) f - 1 ( x) = tan ( x) is the inverse of f ( x) = arctan ( x) f ( x) = arctan ( x) g ( f ( x)) g ( f ( x)) Evaluate g ( f ( x)) g ( f ( x)) by substituting in the value of f f into g g. arcsin ( sin ( x)) arcsin ( sin ( x)) Since g ( f ( x)) = x g ( f ( x)) = x, f − 1 ( x) = arcsin ( x) f - 1 ( x) = arcsin ( x) is the inverse of f ( x) = sin ( x) f ( x) = sin ( x) How to Solve Using an Inverse Matrix; How to Combine Functions; How to Find the Upper or Third Quartile; How to Use the Camera Featur

New Version: https://youtu.be/q6y0ToEhT1EDefine an inverse function. Determine if a function as an inverse function. Determine inverse functions.http://ma.. Mathway currently only computes linear regressions. We are here to assist you with your math questions. You will need to get assistance from your school if you are having problems entering the answers into your online assignment The Inverse Function (Celsius back to Fahrenheit): f-1 (C) = (C × 95) + 32 For you: see if you can do the steps to create that inverse! Inverses of Common Functions STEP ONE: Rewrite f (x)= as y=. If the function that you want to find the inverse of is not already expressed in y= form, simply replace f (x)= with y= as follows (since f (x) and y both mean the same thing: the output of the function): STEP ONE: Swap X and Y Functions. Is a Function; Domain; Range; Vertex; Periodicity; Amplitude; Shift; Frequency; Inverse; Intercepts; Parity; Symmetry; Asymptotes; Critical Points; Inflection Points; Monotone Intervals; Extreme Points; Global Extreme Points; Absolute Extreme; Turning Points; Concavity (new) End Behavior (new) Average Rate of Change (new) Holes (new) Piecewise Functions; Continuity (new) Discontinuity (new

- We have learned that a function f maps x to f (x). The inverse of f is a function which maps f (x) to x in reverse. The inverse of the function f is denoted by f -1. The inverse of a function is found by interchanging its range and domain
- inverse\:y=\frac{x^2+x+1}{x} inverse\:f(x)=x^3; inverse\:f(x)=\ln (x-5) inverse\:f(x)=\frac{1}{x^2} inverse\:y=\frac{x}{x^2-6x+8} inverse\:f(x)=\sqrt{x+3} inverse\:f(x)=\cos(2x+5) inverse\:f(x)=\sin(3x
- Find the Inverse Laplace transforms of functions step-by-step. full pad ». x^2. x^ {\msquare} \log_ {\msquare} \sqrt {\square} \nthroot [\msquare] {\square} \le. \ge
- The inverse function of $f$ is simply a rule that undoes $f$'s rule (in the same way that addition and subtraction or multiplication and division are inverse operations.) Consequently, the range and domain of $f$ and $f^{-1}$ simply switch

Get the free Inverse Function Calculator - Math101 widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha Usually, to find the Inverse Laplace transform of a function, we use the property of linearity of the Laplace transform. Just perform partial fraction decomposition (if needed), and then consult the table of Laplace transforms. Your input: find. $$$. \mathcal {L}^ {-1}\left (\frac {5} {s^ {2} + 2 s + 10}\right) $$$ Inverse function calculator helps in computing the inverse value of any function that is given as input. To recall, an inverse function is a function which can reverse another function. It is also called an anti function. It is denoted as: f(x) = y ⇔ f − 1 (y) = x

Inverse function definition by Duane Q. Nykamp is licensed under a Creative Commons Attribution-Noncommercial-ShareAlike 4.0 License. For permissions beyond the scope of this license, please contact us Sal introduces arcsine, which is the inverse function of sine, and discusses its principal range

- These inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios. Let's discuss each inverse trigonometric function in detail. arcsine. arcsine function is an inverse of the sine function denoted by sin-1 x. It returns the angle whose sine corresponds to the provided number
- Learn how to find the inverse of a linear function. A linear function is a function whose highest exponent in the variable(s) is 1. The inverse of a funct..
- Micro for Business Tutorial on Algebra given by Eva Szatmari from the School of Business, Economics and Informatics at Birkbeck, University of London.Video P..
- Mathway Calculate power function The Calculator can find derivatives using the sum. It aims to solve recurrence relations where the recurrence relation is a linear Solve the recurrence relation for the specified function. Relations Try the free Mathway calculator and problem solver below to practice various math topics
- Inverse function of y=1/x is y=1/x itself. As y=1/x, we have x=1/y Hence, inverse function of y=1/x is y=1/x itself and it is obviously a function
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Properties of Logarithms -..
- ing if Linear. Rewriting as an Equation. Rewriting as y=mx+b. Solving Function Systems. Find the Behavior (Leading Coefficient Test) Finding Ordered Pair Solutions

- Related articles. How to Find Sine, Cosine, and Tangent ; How to Solve Using an Inverse Matrix; How to Combine Functions; How to Find the Upper or Third Quartil
- Learn how to find the inverse of a quadratic function. A quadratic function is a function whose highest exponent in the variable(s) of the function is 2..
- This algebra 2 and precalculus video tutorial explains how to find the inverse of a function using a very simple process. First, replace f(x) with y. Next,..

Notice that it is not as easy to identify the inverse of a function of this form. So, consider the following step-by-step approach to finding an inverse: Step 1: Replace f ( x) with y. (This is simply to write less as we proceed) y = x + 4 3 x − 2. Step 2: Switch the roles of x and y. x = y + 4 3 x − 2 Inverse Functions. A series of free, online Intermediate Algebra Lessons or Algebra II lessons. Videos, worksheets, and activities to help Algebra students. In these lessons, we will learn. the definition of one-to-one functions. the definition of inverse functions. how to find the inverse of a function algebraically

Inverse Function Calculator inverts function with respect to a given variable.Inverse function for a function y=f(x) is such function x=g(y) that g(f(x))=x for all values of x where f is defined. An important property of the inverse function is that inverse of the inverse function is the function itself Compute the inverse Laplace transform of 1/ (s-a)^2. By default, the independent and transformation variables are s and t , respectively. syms a s F = 1/ (s-a)^2; ilaplace (F) ans = t*exp (a*t) Specify the transformation variable as x. If you specify only one variable, that variable is the transformation variable Graph an Inverse Function. Summary: After you graph a function on your TI-83/84, you can make a picture of its inverse by using the DrawInv command on the DRAW menu. For this illustration, let's use f(x) = √ x−2, shown at right.Though you can easily find the inverse of this particular function algebraically, the techniques on this page will work for any function 0 out of 1 found this helpful. Facebook; Twitter; LinkedIn; Have more questions? Submit a reques

Calculate the inverse function of the given function simply by following the below given steps. Let us take one function f (x) having x as the variable. Consider that y is the function for f (x) Swap the variables x and y, then the resulting function will be x. Now, solve the equation x for y. Find the value of y * Description*. The inverseKinematics System object™ creates an inverse kinematic (IK) solver to calculate joint configurations for a desired end-effector pose based on a specified rigid body tree model. Create a rigid body tree model for your robot using the rigidBodyTree class. This model defines all the joint constraints that the solver enforces

Inverse function calculator. The inverse function of: Submit: Computing... Get this widget. Build your own widget. Verifying Inverse Functions For every function, there is an inverse function. For every inverse function, there is a function. In order to verify this algebraically, one must substitute f(x) into f-1 (x) and then f-1 (x) into f(x). If this results in both expressions equaling x, then the functions are inverses of one another Mathway Calculator Widget. Share this page to Google Classroom. Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations ** Inverse functions undo each other when we compose them**. We can compose functions by making the output of one function the input of another one. This simple-yet-rich idea opens up a world of fascinating applications.** Inverse functions undo each other when we compose them** If the function f (x) = a x + b has its own inverse then the ordered pair (a,b) can be This question has multiple correct options. A (1,0) B (-1,0) C (-1,1) D (1,1) Medium. Answer. Correct option is . A (1,0) B (-1,0) C (-1,1) f (x) = a (x) +

A function has an inverse function if it is one-to-one (or invertible), which means it passes both vertical and horizontal line tests. A function that has an inverse or is one-to-one is strictly monotonic (either increasing or decreasing) for its entire domain. Monotonic Functions in an Interval Note that if a function has an inverse that is also a function (thus, the original function passes the Horizontal Line Test, and the inverse passes the Vertical Line Test), the functions are called one-to-one, or invertible. This is because there is only one answer for each question for both the original function and the inverse. Example 2: Sketch the graphs of f (x) = 3x2 - 1 and g ( x) = x + 1 3 for x ≥ 0 and determine if they are inverse functions. Step 1: Sketch both graphs on the same coordinate grid. Step 2: Draw line y = x and look for symmetry. If symmetry is not noticeable, functions are not inverses. If symmetry is noticeable double check with Step 3 A restriction of the polynomial is a new function, with one of those intervals as its domain, whose values agree with the values of the polynomial on that interval. Those functions are one-to-one on those intervals and have inverses. The graphs of a function and its inverse are symmetric in the line y = x. This Demonstration plots the graphs of. Derivatives of Inverse Trig Functions. Examples: Find the derivatives of each given function. f (x) = -2cot -1 (x) g (x) = 5tan -1 (2 x) Show Video Lesson. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step.

Free piecewise functions calculator - explore piecewise function domain, range, intercepts, extreme points and asymptotes step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy Online Derivative Calculator. Enter a valid algebraic expression to find the derivative. Not sure what that means? Type your expression (like the one shown by default below) and then click the blue arrow to submit. Choose Find the Derivative from the menu and click to see the result Functions f and g are inverses if f(g(x))=x=g(f(x)). For every pair of such functions, the derivatives f' and g' have a special relationship. Learn about thi..

The MINVERSE function returns the inverse matrix for a matrix stored in an array. Array can be given as a cell range, such as A1:C3; as an array constant, such as {1,2,3;4,5,6;7,8,9}; or as a name for either of these. Inverse matrices, like determinants, are generally used for solving systems of mathematical equations involving several variables. The product of a matrix and its inverse is the. Inverse of a Function. Doing a function and then its inverse will give us back the original value: When the function f turns the apple into a banana, Then the inverse function f-1 turns the banana back to the apple . Here we have the function f(x) = 2x+3, written as a flow diagram

Inverse Trigonometric Functions In a problem where two trig functions are not inverses of each other (also known as inverse trigonometric functions), (1) replace the inverse function with a variable (which represents an angle), (2) use the definition of the inverse function to draw the angle in the unit circle and identify one coordinate Compute the inverse Z-transform of 1/ (a*z). By default, the independent and transformation variables are z and n , respectively. syms z a F = 1/ (a*z); iztrans (F) ans = kroneckerDelta (n - 1, 0)/a. Specify the transformation variable as m. If you specify only one variable, that variable is the transformation variable 4.6- Inverse Trig Functions. Inverse functions are another topic that looks incredibly difficult but it reality it quite easy. Te first step and really only tool you need is the chart bellow. You need to memorize this chart. There is no other way around it. Once you memorize this, the inverse math part is incredibly easy

Verifying inverse functions by composition: not inverse. Sal composes f (x)=2x-3 and g (x)=½x+3, and finds that f (g (x)) ≠ g (f (x)) ≠ x, which means the functions are not inverses. This is the currently selected item The inverse Laplace transform is exactly as named — the inverse of a normal Laplace transform. An inverse Laplace transform can only be performed on a function F (s) such that L {f (t)} = F (s) exists. Because of this, calculating the inverse Laplace transform can be used to check one's work after calculating a normal Laplace transform Trigonometric Equation Calculator. \square! \square! . Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us Areacosine or inverse hyperbolic cosine. Increasing function. Function is defined only for x greater or equal 1. Areatangent or inverse hyperbolic tangent. Odd, continuously increasing function. Function is defined only for x greater then -1 and less then +1. Areacotangent or inverse hyperbolic cotangent. Odd, continuously decreasing function Intro to arcsine. This is the currently selected item. Intro to arctangent. Intro to arccosine. Practice: Evaluate inverse trig functions. Restricting domains of functions to make them invertible. Domain & range of inverse tangent function. Using inverse trig functions with a calculator. Inverse trigonometric functions review

Calculate limits, integrals, derivatives and series step-by-step. \square! \square! . Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us Ejemplos paso a paso. Relations. Determining if the Relation is a Function. Finding the Domain and Range of the Relation. Finding the Inverse of the Relation. Finding the Inverse. Determining if One Relation is the Inverse of Another. Determining if Surjective (Onto details: some exact evaluations of the arctan(1/a) function. Education Details: 3π/16.All of thes examples represent arctan gents with value s of bπ/2 n , where b and n are integers.One can also generate the value s of a for terms such as 2π/3 or 5π/6.These follow by use of the known exact value s π/6= arctan [1/ sqrt(3)] and π/3= arctan. Inverse Trigonometric Functions In a problem where two trig functions are not inverses of each other (also known as inverse trigonometric functions), (1) replace the inverse function with a variable (which represents an angle), (2) use the definition of the inverse function to draw the angle in the unit circle and identify one coordinate, (3.

1.7 - Inverse Functions Notation. The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced f inverse. Although the inverse of a function looks like you're raising the function to the -1 power, it isn't Inverse Function. For any one-to-one function f(x) = y, a function f − 1(x) is an inverse function of f if f − 1(y) = x. This can also be written as f − 1(f(x)) = x for all x in the domain of f. It also follows that f(f − 1(x)) = x for all x in the domain of f − 1 if f − 1 is the inverse of f. The notation f − 1 is read f. How to Use Inverse Functions Graphing Calculator. Enter a formula for function f (2x - 1 for example) and press Plot f (x) and Its Inverse. Three graphs are displayed: the graph of function f (blue) that you input, the line y = x (black), and the graph (red) of the inverse. The variable in the expression of the function is the small letter x The inverse function, denoted f -1, of a one-to-one function f is defined as. f -1 (x) = { (y,x) | such that y = f (x)} Note: The -1 in f -1 must not be confused with a power. If function f is not a one-to-one then it does not have an inverse. More discussions on one to one functions will follow later

How to Find the **Inverse** of a **Function** 1 - Cool Math has free online cool math lessons, cool math games and fun math activities. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too Mathway can be that extra eye to help double-check your work. Mathway's math solver is an excellent tool to check your work for free. Just type in the math problem using its prescribed syntax and it will give you the correct answer. Note: If you want more help, and therefore, would want to see how Mathway solves the problem step by step. Thousands Maths Online. Home; All Calculators. Definite Integral Calculator; Derivative Calculator; Double Integral Calculato Inverse Functions . 1.1k plays . 10 Qs . Maths . 2.3k plays . 10 Qs . Multiplying Radicals with Variables . 1.4k plays . Quiz not found! BACK TO EDMODO. Menu. Find a quiz. All quizzes. All quizzes. My quizzes. Reports. Create a new quiz. 0. Join a game Log in Sign up. View profile. Have an account? Log in now. Create a new quiz. Find a quiz; My. Questions on Inverse Functions with Solutions. Questions on inverse functions are presented along with detailed solutions and explanations. The questions below will help you develop the computational skills needed in solving questions about inverse functions and also gain deep understanding of the concept of inverse functions

The trigonometric functions in MATLAB ® calculate standard trigonometric values in radians or degrees, hyperbolic trigonometric values in radians, and inverse variants of each function. You can use the rad2deg and deg2rad functions to convert between radians and degrees, or functions like cart2pol to convert between coordinate systems Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! The Inverse Laplace Transf.. Finding the Inverse of a Function. Given the function f (x) f ( x) we want to find the inverse function, f −1(x) f − 1 ( x). First, replace f (x) f ( x) with y y. This is done to make the rest of the process easier. Replace every x x with a y y and replace every y y with an x x. Solve the equation from Step 2 for y y How to Solve Piecewise Functions. If playback doesn't begin shortly, try restarting your device. Videos you watch may be added to the TV's watch history and influence TV recommendations. To avoid this, cancel and sign in to YouTube on your computer

An inverse function essentially undoes the effects of the original function. If f (x) says to multiply by 2 and then add 1, then the inverse f (x) will say to subtract 1 and then divide by 2. If you want to think about this graphically, f (x) and its inverse function will be reflections across the line y = x Find the inverse function, its domain and range, of the function given by f(x) = √(x - 1) Solution to example 1. Note that the given function is a square root function with domain [1 , + ∞) and range [0, +∞). We first write the given function as an equation as follows y = √(x - 1 The Lesson A function and its inverse function can be plotted on a graph. If the function is plotted as y = f(x), we can reflect it in the line y = x to plot the inverse function y = f −1 (x). Every point on a function with Cartesian coordinates (x, y) becomes the point (y, x) on the inverse function: the coordinates are swapped around. How to Find the Inverse of a Function Using a Grap Since y = sin -1 x is the inverse of the function y = sin x, the function y = sin-1 x if and only if sin y = x.But, since y = sin x is not one-to-one, its domain must be restricted in order that y = sin-1 x is a function.. To get the graph of y = sin-1 x, start with a graph of y = sin x.. Restrict the domain of the function to a one-to-one region - typically is used (highlighted in red at. Calculates the inverse hyperbolic functions asinh(x), acosh(x) and atanh(x). x 6digit 10digit 14digit 18digit 22digit 26digit 30digit 34digit 38digit 42digit 46digit 50digi

A Transpose/Unzip Function in Python I've used the zip() function from the numpy library to sort tuples and now I have a list containing all the tuples. I had since modified that list and now I would like to restore the tuples so I can use my data Improve your math knowledge with free questions in Find values of inverse functions from tables and thousands of other math skills Problems on inverse trigonometric functions are solved and detailed solutions are presented. Also exercises with answers are presented at the end of this page. We first review some of the theorems and properties of the inverse functions. Theorem 1 Function Grapher and Calculator. Description:: All Functions. Description. Function Grapher is a full featured Graphing Utility that supports graphing up to 5 functions together. You can also save your work as a URL (website link). Usage To plot a function just type it into the function box. Use x as the variable like this

Details (Matrix multiplication) With help of this calculator you can: find the matrix determinant, the rank, raise the matrix to a power, find the sum and the multiplication of matrices, calculate the inverse matrix. Just type matrix elements and click the button. Leave extra cells empty to enter non-square matrices ** 210°, 330° Using your calculator, press shift sin (1/2) and it will give you 30**. (Always ignore the negative when you are doing the inverse!) But since this is a negative, you cannot just write 30° as your final answer. Using the ASTC rule, you know that for sin to be positive it has to be in Quadrant 1 and 2. But since this is a negative it has to be the complete opposite This section covers: Direct or Proportional Variation Inverse or Indirect Variation Joint and Combined Variation Partial Variation More Practice When you start studying algebra, you will also study how two (or more) variables can relate to each other specifically. The cases you'll study are: Direct Variation, where one variable is a constant multiple of another Direct, Inverse, Joint and. Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels Summary. Function Composition is applying one function to the results of another. (g º f) (x) = g (f (x)), first apply f (), then apply g () We must also respect the domain of the first function. Some functions can be de-composed into two (or more) simpler functions

y = x^2-2 which is the inverse function of y = sqrt(x+2) Selection C inverse equation is the same as the original equation. graph of this equation is shown below: The line y = -x-2 is a reflection about the line y = x which is a definition of inverse function. Take any point (x,y) on the line y = -x-2 above the line y = x If you've done the symbolic composition (the composition with the formulas) correctly, you'll get the same values either way, regardless of the value you pick for x. This can be a handy way of checking your work. Given f ( x) = 2 x + 3 and g ( x) = - x2 + 5, find ( g o f ) ( x). There is something you should note from these two symbolic. Advanced Math Solutions - Integral Calculator, inverse & hyperbolic trig functions In the previous post we covered common integrals ( click here ). There are a few more integrals worth mentioning before we continue with integration by parts; integrals involving inverse & hyperbolic trig functions NORMSINV function Description. Returns a Standardized Normal deviate. NORMSINV(P) returns the standardized Normal deviate z corresponding with the one-tailed probability P. P must be a value between 0 and 1 (0< P <1). NORMSINV is the inverse function of the NORMSDIST function. Examples. NORMSINV(0.025) returns -1.96 (rounded). NORMSINV(0. As functions of a complex variable, inverse hyperbolic functions are multivalued functions that are analytic, except at a finite number of points. For such a function, it is common to define a principal value, which is a single valued analytic function which coincides with one specific branch of the multivalued function

Practial Algebra Lessons: Purplemath's algebra lessons are informal in their tone, and are written with the struggling student in mind. Don't worry about overly-professorial or confusing language! These math lessons emphasize the practicalities rather than the technicalities, demonstrating dependably helpful techniques, warning of likely trick test questions, and pointing out common student. Derivatives and Integrals of Inverse Trig Functions. We learned about the Inverse Trig Functions here, and it turns out that the derivatives of them are not trig expressions, but algebraic. When memorizing these, remember that the functions starting with c are negative, and the functions with tan and cot don't have a square root Use Partial Fraction Composition. Solve Rational Inequalities. Solve Quadratic Inequalities. Solve Linear Inequalities. Solve Function Systems. Find the Symmetry. Find the Behavior Leading Coefficient Test. Find the Anti Derivative. Determine Odd and Even Functions ** The procedure to use the inverse trig functions calculator is as follows: Step 1: Enter the value in the input field**. Step 2: Now click the button Calculate to get the result. Step 3: Finally, the values of inverse trig functions will be displayed in the output field And this is the Ceiling Function: The Ceiling Function. The Int Function. The Int function (short for integer) is like the Floor function, BUT some calculators and computer programs show different results when given negative numbers: Some say int(−3.65) = −4 (the same as the Floor function

Certain inverse functions, like the inverse trig functions, have limited domains as well. Since the sine function can only have outputs from -1 to +1, its inverse can only accept inputs from -1 to +1. The domain of inverse sine is -1 to +1 Online arcsin(x) calculator. Inverse sine calculator. Enter the sine value, select degrees (°) or radians (rad) and press the = button Inverse Log Formula. The following formula is used to calculate the inverse log of a number and base. x = log b-1 (y) = b y. Where x is the value you are calculating; b is the base; and y is the number to take the log of; Inverse Log Definition. An inverse log is defined as the anti-log of a log function raised to a negative value. Inverse Log. The Beta function is a unique function and is also called the first kind of Euler's integrals. The beta function is defined in the domains of real numbers. The notation to represent it is β. The beta function is denoted by β(p, q), Where the parameters p and q should be real numbers Find inverse functions and relations Q. Families of functions. 1. Function transformation rules 2. Translations of functions 3. Reflections of functions 4. Dilations of functions 5. Transformations of functions 6. Describe function transformations R. Variation. 1. Write and solve direct variation equations.

Mathway Support; Submit a request Submit a request Your email address. Subject. Description. Please enter the details of your request. A member of our support staff will respond as soon as possible. Attachments Add file or drop files here. Graphing Cosine Function - Varsity Tutors. Education Details: Amplitude and Period a Cosine Function The amplitude of the graph of y = a cos ( b x ) is the amount by which it varies above and below the x -axis. Amplitude = | a | The period of a cosine function is the length of the shortest interval on the x -axis over which the graph › Verified 4 days ag

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