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Precalculus
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Verifying inverse functions in Exercise 9-16, show that f and g are inverse functions (a) analytically and (b) graphically.

 

 

such that x greater than or equal to zero.

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Angelo Torreno
Angelo TorrenoLv4
30 Oct 2020

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Functions That are their own Inverse If a function f is its own inverse then the graph of f is symmetric about the line y=x. (a) Graph the give function. (b) Does the graph indicate that f and f-1 are the same function? (c) Find the function f-1. Use your result to verify your answer to part (b).

 

Consider the following rational functions:

  

(a) Which of these rational functions has a horizontal asymptote?

(b) Which of these functions has a slant asymptote?

(c) Which of these functions has no vertical asymptote?

(d) Which of these functions has a "hole"?

(e) What are the asymptotes of the function r(x)?

(f) Graph the function y = u(x), showing clearly all the asymptotes, x-intercepts, and y-intercepts that the function may have.

(g) Use long division to find a polynomial P that has the same end behavior as t. Graph both P and t to verify that they have the same end behavior. 

Consider the following rational functions:

 

(a) Which of these rational functions has a horizontal asymptote?

(b) Which of these functions has a slant asymptote?

(c) Which of these functions has no vertical asymptote?

(d) Which of these functions has a "hole"?

(e) What are the asymptotes of the function r(x)?

(f) Graph the function y = u(x), showing clearly all the asymptotes, x-intercepts, and y-intercepts that the function may have.

(g) Use long division to find a polynomial P that has the same end behavior as t. Graph both P and t to verify that they have the same end behavior. 

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