Graphing Rational Functions: Key Concepts and Techniques

What is the first step in finding the y-intercept of a rational function?

• Set the numerator equal to zero

• Compare the degrees of the numerator and denominator

• Set the denominator equal to zero

• Plug 0 into the equation for x

If the degree of the numerator is greater than the degree of the denominator, what can be said about the horizontal asymptote?

• It is at y = 1

• It is the ratio of the leading coefficients

• There is no horizontal asymptote

• It is at y = 0

How do you find the x-value of a hole in a rational function?

• Plug 0 into the equation for x

• Set the denominator equal to zero

• Set the canceled factor equal to zero

• Set the numerator equal to zero

What is the next step after factoring the numerator and denominator of a rational function?

• Find the vertical asymptote

• Find the y-intercept

• Determine the horizontal asymptote

• Cancel out common factors

In the first example, what is the horizontal asymptote of the function?

• y = 0

• y = -1

• y = 1

• y = 2

What is the x-intercept of the function in the first example?

• 0, 0

• 2, 0

• 3, 0

• 1, 0

In the second example, what is the y-intercept of the function?

• 0, 3

• 0, 2

• 0, 5/8

• 0, 1

What is the vertical asymptote in the second example?

• x = 5

• x = 8

• x = 0

• x = -3

In the final examples, what is the horizontal asymptote of the function?

• y = 1

• y = 2

• y = 0

• y = -1

What is the x-intercept of the function in the final example?

• 5, 0

• 2, 0

• 1, 0

• 0, 0