Question

place the steps to sketch the graph of a rational function in the appropriate order.
find the functions zeros and vertical asymptotes, and plot them on a number line.
use test numbers to find where the function is positive and where it is negative.
sketch the functions graph, plotting additional points as guides as needed.
choose test numbers to the left and right of each of these places, and find the value of the function at each test number.

Explanation:

Step1: Find zeros and asymptotes

Find the function's zeros and vertical asymptotes, and plot them on a number line.

Step2: Choose test numbers

Choose test numbers to the left and right of each of these places, and find the value of the function at each test number.

Step3: Determine sign

Use test numbers to find where the function is positive and where it is negative.

Step4: Sketch graph

Sketch the function's graph, plotting additional points as guides as needed.

Answer:

1. Find the function's zeros and vertical asymptotes, and plot them on a number line.
2. Choose test numbers to the left and right of each of these places, and find the value of the function at each test number.
3. Use test numbers to find where the function is positive and where it is negative.
4. Sketch the function's graph, plotting additional points as guides as needed.