Question

question 28 of 42
what is the first step in sketching the graph of a rational function?

a. sketching the functions graph and plotting additional points as guides when needed

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

c. choosing test numbers to the left and right of each of the functions zeros and finding the value of the function at each test number

d. finding the functions zeros and vertical asymptotes and plotting them on a number line

Explanation:

To sketch a rational function's graph, the first step is to identify key features like zeros (where numerator is zero) and vertical asymptotes (where denominator is zero, excluding holes). Plotting these on a number line helps define the function's behavior. Option A is later steps (plotting additional points/sketching). Option B and C involve test numbers, which come after identifying zeros and asymptotes. So D is the first step.

Answer:

D. Finding the function’s zeros and vertical asymptotes and plotting them on a number line