Question

The figure below shows the graph of a rational function $f$. It has vertical asymptotes $x = 2$ and $x = -5$, and horizontal asymptote $y = 0$. The graph does not have an $x$-intercept, and it passes through the point $(1, -1)$. The equation for $f(x)$ has one of the five forms shown below. Choose the appropriate form for $f(x)$, and then write the equation. You can assume that $f(x)$ is in simplest form.

Name: the figure below shows the graph of a rational function f it has vertical asymptotes x 2 and x 5 and horizontal asymptote y 0 the graph does not have an x intercept and it passes through the 10216
Uploaded: 2023-09-10T00:42:16-08:00
Duration: 2 min 5 s
Channel: Gregory Higby
Description: the figure below shows the graph of a rational function f it has vertical asymptotes x 2 and x 5 and horizontal asymptote y 0 the graph does not have an x intercept and it passes through the 10216

          The figure below shows the graph of a rational function $f$.
It has vertical asymptotes $x = 2$ and $x = -5$, and horizontal asymptote $y = 0$.
The graph does not have an $x$-intercept, and it passes through the point $(1, -1)$.
The equation for $f(x)$ has one of the five forms shown below.
Choose the appropriate form for $f(x)$, and then write the equation.
You can assume that $f(x)$ is in simplest form.

the figure below shows the graph of a rational function f it has vertical asymptotes x 2 and x 5 and horizontal asymptote y 0 the graph does not have an x intercept and it passes through the 10216

Added by Josefina N.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Gregory Higby

09/10/2023

Step 1

Since there are vertical asymptotes at $x=2$ and $x=-5$, the denominator must have factors $(x-2)$ and $(x+5)$. Since there is no $x$-intercept, the numerator has no real roots. Show more…

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The figure below shows the graph of a rational function $f$. It has vertical asymptotes $x = 2$ and $x = -5$, and horizontal asymptote $y = 0$. The graph does not have an $x$-intercept, and it passes through the point $(1, -1)$. The equation for $f(x)$ has one of the five forms shown below. Choose the appropriate form for $f(x)$, and then write the equation. You can assume that $f(x)$ is in simplest form.