Graphing Techniques in W23B.V

What is the first step in graphing rational functions?

• Finding the vertical asymptotes

• Finding the horizontal asymptotes

• Finding the x-intercepts

• Simplifying the expression completely

How do you find the x-intercepts of a rational function?

• Set the entire function equal to zero and solve for y

• Set the entire function equal to zero and solve for x

• Set the denominator equal to zero and solve for x

• Set the numerator equal to zero and solve for x

What is the y-intercept of the function f(x) = 1/(x + 4)?

• (0, 4)

• (0, 1/4)

• (1, 0)

• (4, 0)

How do you find the vertical asymptotes of a rational function?

• Set the entire function equal to zero

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set the numerator and denominator equal to zero

What is the horizontal asymptote of the function f(x) = 1/(x + 4)?

• y = 1

• y = -1

• y = 0

• None

Where do holes in the graph of a rational function occur?

• Where factors cancel out

• Where the denominator is zero

• Where the numerator is zero

• Where the function is undefined

What is the domain of the function f(x) = 1/(x + 4) considering the hole and vertical asymptote?

• All real numbers except x ≠ 5 and x ≠ 4

• All real numbers except x ≠ 4

• All real numbers except x ≠ -5 and x ≠ -4

• All real numbers except x ≠ -4

What is the range of the function f(x) = 1/(x + 4) considering the hole and horizontal asymptote?

• All real numbers except y ≠ -1 and y ≠ 0

• All real numbers except y ≠ 1 and y ≠ 0

• All real numbers except y ≠ -1

• All real numbers except y ≠ 0

What is the first step in simplifying the function x^3 - 2x^2 - 8x / 3x^2 - 27?

• Find the vertical asymptotes

• Factor out the common terms

• Find the x-intercepts

• Find the y-intercepts

What is the horizontal asymptote of the function x^3 - 2x^2 - 8x / 3x^2 - 27?

• None

• y = -1

• y = 1

• y = 0