Exploring Graphing Techniques for Rational Functions

What is the horizontal asymptote of a rational function where the degree of the numerator is less than the degree of the denominator?

• No horizontal asymptote

• x = 0

• y = 1

• y = 0

How do you find the vertical asymptote of the function f(x) = 2/(x+4)?

• Set the numerator equal to zero

• Set x equal to -4

• There is no vertical asymptote

• Set the denominator equal to zero

For the function f(x) = 2/(x+4), what is the x-intercept?

• There is no x-intercept

• x = -4

• x = 2

• x = 0

What is the y-intercept of the function f(x) = 2/(x+4)?

• (0, 0.25)

• (0, 2)

• (0, 1)

• (0, 0.5)

In the function f(x) = (3x^2 - 9x) / (x^3 - 7x^2 + 12x), after simplification, what causes the holes in the graph?

• Factors in the numerator

• Factors in the denominator

• Common factors in the numerator and denominator

• The degree of the polynomial

What is the vertical asymptote of the simplified function 3/(x-4)?

• x = -4

• x = 4

• x = 0

• x = 3

For the function f(x) = (3x^2 - 9x) / (x^3 - 7x^2 + 12x), what is the y-intercept?

• (0, 0.75)

• (0, -0.75)

• (0, 3)

• There is no y-intercept

How is the domain of a rational function determined?

• By finding the x-intercepts

• By setting the numerator to zero

• By the degree of the function

• By identifying the vertical asymptotes and holes

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

• y = 1

• y = 0

• y = 2

• There is no horizontal asymptote

For the function 2x - 8 / x - 2, what is the correct domain?

• x < 2

• x > 2

• x ≠ 2

• All real numbers