Question

Place the steps to sketch the graph of a rational function in the appropriate order.swap_vertFind the function's zeros and vertical asymptotes, and plot them on a number line.swap_vertUse test numbers to find where the function is positive and where it is negative.swap_vertChoose test numbers to the left and right of each of these places, and find the value of the function at each test number.

Answer 1

Explanation:

The correct answer is:

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

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

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

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

Answer 2

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define a rational function

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials

STEP 2: list the steps

Explain how to plot the graph

Whether the sign changes at an asymptote or root is determined by its multiplicity. An asymptote or root of odd degree will be a place where the sign changes. If the degree is even, the sign will be the same on either side of the asymptote or root.

This means that if you determine multiplicity in the first step (F), you can essentially skip the 2nd and 3rd steps by looking at the sign of the leading term of the function. That sign will determine the function value for large positive values of the variable, and you can track sign changes as you go left across each of the points you found in the first step.

Hence, the correct arrangement will be: