Chapter 4.5, Problem 16AYU

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

$R\left(x\right)=\frac{2x+4}{x-1}$

To determine

To find: Ananlyze the given function.

Answer to Problem 16AYU

Explanation of Solution

Given:

$R\left(x\right) = \frac{2x + 4}{x - 1}$

Step 1: Factor $\text{R}$ to get

$R\left(x\right) = \frac{2x + 4}{x - 1}$

That is $x = 1$.

The domain $\left\{x\text{|}x \ne 1\right\}$

Step 2: $\text{R}$ is in lowest terms.

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

$y\text{-intercepts}$ is $4$

$x\text{-intercept}$ is $-2$

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

$x = 1$.

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

Horizontal asymptote: $y = 0$, intersected at $\left(0, 0\right)$.

Step 6: Graph $\text{R}$ using a graphing utility.

Step 7: