Degrees in Polynomial and Rational Functions

Arjun is trying to find the x-intercepts of a rational function that models the profit of a company. How should he determine the x-intercepts of this function?

• Set the denominator equal to zero and solve for x.

• Set the whole function equal to zero and solve for x.

• Take the derivative of the function and find the x-values where the derivative is zero.

• Set the numerator equal to zero and solve for x.

Tags

PC.F.4.5 

Select all the following statements that are true.

• Vertical asymptote at x=1

• Vertical asymptote at x=0

• No vertical asymptote

• Hole at (-1, 0)

• Hole at (1, -1)

Tags

PC.F.4.5 

Find the horizontal asymptote of f(x)

• None

• y=6

• y=1/3

• y=3

Tags

PC.F.4.5 

Choose the correct graph that matches with the equation.

• A

• B

• C

• D

Tags

PC.F.4.5 

Oliver and Daniel are working on a project to model the water flow through a pipe system using a rational function. How do they determine the domain of this function?

• Find the values of x that make the numerator non-zero.

• Find the values of x that make the denominator zero.

• Find the values of x that make the function undefined.

• Find the values of x that make the denominator non-zero.

Tags

PC.F.4.5 

Maya, Avery, and Sophia are studying the end behavior of rational functions in their math class. What are the possible types of end behavior for a rational function they might encounter?

• Approaching zero

• Approaching a constant value

• Approaching a finite number

• Approaching positive infinity or approaching negative infinity

Tags

PC.F.4.5 

Graph the function.

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Let f be a rational function that is graphed in the xy-plane. Consider x = 1 and x = 7. The polynomial in the numerator of f has a zero at x = 1 and does not have a zero at x = 7. The polynomial in the denominator of f has zeros at both x = 1 and x = 7. The multiplicities of the zeros at x = 1 in the numerator and in the denominator are equal. Which of the following statements is true?

• The graph of f has holes at both x = 1 and x = 7

• The graph of f has a vertical asymptote at x = 1 and a hole at x = 7

• The graph of f has a hole at x = 1 and a vertical asymptote at x = 7

• The graph of f has vertical asymptotes at both x = 1 and x = 7

Graph the function.

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