Can a one-to-one function and its inverse be equal? Whatmust be true about the graph of f for this to happen? Givesome examples to support your conclusion.

Q: Sketch the graph of the function. Be sure to label three points on the graph. f(x) = 1/x

A: Given f(x)=1x x=1 ⇒f(x)=11=1⇒(1,1)x=-1 ⇒f(x)=1-1=-1⇒(-1,-1)x=2 ⇒f(x)=12=0.5⇒(2,0.5)x=-2…

Q: Now, let's put it all together to graph the entire function, f(x) = 10. Create a table for f(x) =…

A: Given that: f(x)=1x

Q: Obtain the graph of the inverse function from the graph of thefunction

A:

Q: Suppose you are given a formula for a function fpxq, and you are asked to find all the critical…

A: Suppose, Given - a formula for a function f(x) Critical Points: Critical point of a function are the…

Q: The distance from Casisang National High School to Misamis Oriental General High School is 20 km.…

A:

Q: List the various rules that allow us to differentiate constant functions,power functions,…

A: To explain: The differentiation rule: Explanation: The constant rule is used to differentiate…

Q: How would you define an inverse function in your own words? Please write as short as possible 

A:

Q: Make a function that violates Clairault's Theorem. Explain why it does. Show how you got it.

A:

Q: Only functions whose graphs pass the ___________ _____ test will have an inversethat is also a…

A: To Determine: Only functions whose graphs pass the ___________ _____ test will have an inversethat…

Q: What is the purpo

A: To determine: Purpose on adding h to the function.

Q: 3) Without a graph, how can one show differentiability of a function at apoint?

A: With out the graph, to show the differentiablity of a function at a point we have to use the…

Q: What is the domain and range of f from the graph above?

A: Consider the given graph.

Q: Does the following represent a function?

A:

Q: Use the graph of f to draw the graph of its inverse function.

A:

Q: Verify the natural domains and associated ranges of some simple functions.?

A: To verify: Domain and its associated range of some functions.

Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

A:

Q: Sketch a graph of the function f(x) 2 sin 6- up 2- -8 -7 -6 -5 -4 -3 -2 -1 4 7. 8 -2 -4 2)

A: graph of sinx   graph of sinπ2x   graph of  -2sinπ2x   graph of -2sinπ2x-2

Q: Give an example to explore numerically how a function behaves near a particular point at which we…

A: Solution: Consider y = f(x) = 1/x is the function Since at x = 0, this function is going to be…

Q: How can the composite function be evaluated?

A: To explain how the composite function can be evaluated.

Q: Identify the function whose graph appears above. f(x) 3D %3D

A: The given graph appears to be tangent function.

Q: How does  a function behave near a particular point at which we cannotdirectly evaluate the…

A: To understand the concept we will consider an example

Q: What is the domain of the following function?

A: Given f(x,y) =4-x2-y2 - ln(y-x) + sin(x)Let g(x,y) =4-x2-y2 h(x,y)= ln(y-x) and t(x)=sin(x)

Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

A:

Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

A:

Q: How does one find the domain of a composite function? I am not understanding the process

A: Composition of a function is defined as,

Q: This describe the value of a function as approaches to some value?

A: Since we know that limit of a function f(x) as x approach c, f(x) approaches x as approaches c.

Q: What is a function, in your own words? Give an example to back up your points.

A:

Q: Sketch the graphs of two distinct functions with the property f′(x)=−x^2+x

A:

Q: Does adding a constant term to a function affect the existence of an inverse function? Explain.

A: Does adding a constant term to a function affect the existence of an inverse function? Explain.

Q: How does your relationship with someone special related to the one-to-one and inverse function?

A: We will try and understand one one functions and inverse functions using the relations around…

Q: Sketch the graph of the function by making a table of values. Use a calculator of necessary.

A: f(x)=13x

Q: Sketch the graph of the function by making a table of values. Use a calculator of necessary. f(x) =…

A: f(x) = 2x

Q: Can the graph of a function be symmetric to the x- axis ? Explain why or why not. If a function is…

A: The answer is no. The graph of a function cannot be symmetric to x axis. The definition is as…

Q: sketch the approximate shapes of the graph of the two functions on the same axes without using a…

A:

Q: How would I find a function that models this?

A: From the given table , it is observed that the given table can represents a linear function.

Q: What do the Algebraic functions include?

A: An algebraic function include variables, constants and algebraic operations (such as addition,…

Q: About the Discontinuity of a function, kindly provide 5 Questions about it with solutions.

A: For a function f(x) to be continuous at a point x=a, it must satisfy the two of the following…

Q: Can a function be both even and odd? Give reasons for your answe

A: We know

Q: What is the rangqe of this function?

A: The given graph of the function is:

Q: How can the One-to-One Functions Graphically be identified?

A: If a function has no two ordered pairs with different first coordinates and the same second…

Q: When is the function said to be real-valued?

A: The function is said to be a real valued function if it assigns a real number for each input value…

Q: find the domian of the function. verify your result with a graphing calculator table or graph f(x)=…

A: Given function f(x)=x-2x+3

Q: Under what conditions imposed on functions the sum, difference, product and quotient of function…

A: We have to find the condition for which the sum, difference, product and quotient of function will…

Q: A function is even if the opposite input results in an

A: For even function :f(-x)=f(x)

Q: How are the graphs of a function and its inverse are closely related?

A: The function f(x) and g(x) are the inverses of each other if it satisfies the identity…

Q: Define the term One-to-One Functions?

A: Definition of One-to-One functions:

Q: What is the Horizontal Line Test for One-to-One Functions?

A: we have to define the horizontal line test for One-to-One Functions.

Q: The original and restricted functions are not the same functions.True or false?

A: Given, 'The original and restricted functions are not the same functions.

Q: What is the relationship between the graph of a function and the graphof its inverse?

A: Consider the function fx and inverse of f(x) is represented by f-1x.

Q: Give Definition of Even Function ?

A: A function fx is said to be the even function if it satisfies the condition as, f-x=fx, for any…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: