Rational Function
/ Domain / x- intercepts
r(x) = 0 / y-intercept
x = 0 / Vertical asymptotes
q(x) = 0 / Horizontal asymptote
When x→±∞, r(x)→? / Sketch the graph: Label the aymptotes and intercepts.
1) /
Sign Analysis or Comparison to the Reciprocal Function
2)
/
Sign Analysis or Comparison to the Reciprocal Function

3.1 Extra Practice Handout - Sketching Rational Functions using Reciprocal Functions

3.1: Rational Functions Extra Practice

1. Define a rational function.

2.  Determine which functions are not rational functions. Explain your reasoning.

i) ii) iii) iv)

v) vi)

3. Explain how to determine a vertical asymptote.

4. a) Explain how to determine an horizontal asymptote.

b) How does a horizontal asymptote help to sketch a rational function?

5. Complete the table below.

Rational Function / Domain / Vertical Asymptote(s) / Horizontal Asymptote

6.  a) Describe how the linear function compares to its reciprocal (rational function)?

y = x - 4

b) Sketch both functions on the same grid.

7.  a) Describe how the quadratic function compares to its reciprocal (rational function)?

y = x2 +1

b) Sketch both functions on the same grid.

8.  Explain the end behaviours for each rational function as and as .

a)

b)

9.  As for the rational function , which horizontal asymptote does the right end behavior approach? Explain your reasoning.

a) y = 3 b) y = 2 c) y = 0 d) y = 1.5

Answers:

2.  iii and vi since denominator not a polynomial function

5.

Rational Function / Domain / Vertical Asymptote(s) / Horizontal Asymptote
/ , / x = 4 / Y = 0
/ , / x = -3 / Y = 0
/ , / x = 0.5 / Y = 0
/ / none / Y = 0
/ , / x= 2 and x= -2 / Y = 0
/ , / x = -1 and x = 2 / Y = 0

6b) 7b)

8a) As , and as ,

b) As , and as ,

9. y = 0 since denominator will continue to increase and divide into the numerator which is a constant.