Chapter 4.3, Problem 28AYU

In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function.

$R\left(x\right)=\frac{x^2-x-12}{x+5}$

To determine

To find: Ananlyze the given function.

Answer to Problem 28AYU

Explanation of Solution

Given:

$R\left(x\right) = \frac{x^2 - x - 12}{x + 5}$

Step 1: Factor $F$ to get

$R\left(x\right) = \frac{x^2 - x - 12}{x + 5}$

$R\left(x\right) = \frac{\left(x - 4\right)\left(x + 3\right)}{x + 5}$

That is $x = -5$

The domain $\left\{x\text{|}x \ne -5\right\}$

Step 2: $R$ is in lowest terms

Step 3: Locate the intercepts of the graph. Use multiplicity to determine the bahaviour of the graph of $R$ at each $x\text{-intercept}$.

$y\text{-intercept}$ $\frac{-12}{5}$.

$x\text{-intercept}$ is 4 and $-3$

Step 4: Locate the vertical asymptotes. Determine the behaviour of the graph on either side of each vertical asymptote.

$x = -5$

Step 5: Locate the horizontal or oblique asymptote. Determine points, if any, at which the graph of $R$ intersects this asymptote.

Here oblique asymptote $y = x$, not intersected.

Step 6: Graph $R$ using a graphing utility.

Step 7: