Chapter 11.8, Problem 25PPS

(a)

To determine

To describe: the shape of the graph.

Answer to Problem 25PPS

Therefore, the shape of the function is a line.

Explanation of Solution

Given:

  $f\left(x\right)=\frac{x^2-x-30}{x-6}$

Calculation:

The function is as follows.

  $f\left(x\right)=\frac{x^2-x-30}{x-6}$

In the graphing calculator, press $Y=$ and enter the function.

The display is shown below.

  $\begin{array}{l}Plot1 plot2 plot3\\ \backslash Y_{1}B{\left(X^2-X-30\right)}^{\prime }\left(X-6\right)\\ \backslash Y_2=\\ \backslash Y_3=\\ \backslash Y_4=\\ \backslash Y_5=\\ \backslash Y_6=\end{array}$

Press GRAPH

The display is shown below.

  

The shape of the function is a line.

Conclusion:

Therefore, the shape of the function is a line.

(b)

To determine

To simplify: the given function.

Answer to Problem 25PPS

Therefore, the simplified factor is $x+5$ .

Explanation of Solution

Given:

  $f\left(x\right)=\frac{x^2-x-30}{x-6}$

The objective is to use factoring and simplify the function.

The function is factorized below.

  $\begin{array}{l}f\left(x\right)=\frac{x^2-x-30}{x-6}\\ =\frac{\left(x-6\right)\left(x+5\right)}{x-6}\\ =x+5\end{array}$

Therefore, the simplified factor is $x+5$ .

Conclusion:

Therefore, the simplified factor is $x+5$ .

(c)

To determine

To find: the zeros of the function.

Answer to Problem 25PPS

Therefore, the zeros of the function is $-5$ .

Explanation of Solution

Given: $f\left(x\right)=\frac{x^2-x-30}{x-6}$

The objective is to find the zeros of the function.

Factor the given equation as

  $\begin{array}{l}f\left(x\right)=\frac{x^2-x-30}{x-6}\\ =\frac{\left(x-6\right)\left(x+5\right)}{x-6}\\ =x+5\end{array}$

The zeros of the function is calculated below.

Set $f=0$ and solve for x

  $\begin{array}{l}x+5=0\\ x=-5\end{array}$

Therefore, the zeros of the function is $-5$ .

Conclusion:

Therefore, the zeros of the function is $-5$ .