Chapter 4.5, Problem 50AYU

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

$G\left(x\right)=\frac{2-x}{{\left(x-1\right)}^2}$

To determine

To find: Analyze the given function.

Answer to Problem 50AYU

Explanation of Solution

Given:

$G\left(x\right)=\frac{2-x}{{\left(x-1\right)}^2}$

Step 1: Factor $G$ to get.

$G\left(x\right)=\frac{2-x}{{\left(x-1\right)}^2}$

That is $x=\text{ 1}$.

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

Step 2: $G$ is in lowest terms.

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

$y\text{-intercept}$ 2, $x\text{-intercept}$ 2.

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

vertical asymptote $x=\text{ 1}$.

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

Here horizontal asymptote $y=-1$, not intersected.

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

Step 7: