Rational Function Attributes Test Review 1. Sketch a graph; describe the transformations. Determine the domain and range – write them in both interval and set-builder notation.

= f ( x)

−1 +3 x+7

2. Factor the following rational function; use these factors to predict the location where thechole(s) and asymptotes will be. Then sketch. cIdentify holes (as open circles), asymptotes (ascdotted lines, and intercepts (as solid dots). Determine Domain and write using both Interval and Set-Builder Notations.

f ( x) =

x2 + x 1 − x2

3. Using the following Rational Functions, Identify the following attributes if they are present: a.

g ( x) =

x2 − 4x + 3 x+2

c.

factored form:

zero(s):

hole(s):

hole(s):

Vertical Asymptote(s):

Vertical Asymptote(s):

Horizontal Asymptote(s):

Horizontal Asymptote(s):

y-intercept:

b.

2 x 2 − 18 x2 − 6 x + 9

factored form:

zero(s):

x 2 + 8 x − 20 g ( x) = x−2

c. h( x) =

y-intercept:

e.

d. f ( x) =

( x 2 − 7 x + 12)( x 2 + x − 2) ( x 2 − x − 6)( x 2 − 16)

factored form:

factored form:

zero(s):

zero(s):

hole(s):

hole(s):

Vertical Asymptote(s):

Vertical Asymptote(s):

Horizontal Asymptote(s):

Horizontal Asymptote(s):

y-intercept:

y-intercept:

4. Given the graph, draw the asymptotes as dotted line, write the equation and identify the asymptotes, Domain & Range. a. Equation: b. Vertical Asymptote: c. Horizontal Asymptote: d. y-intercept: e. Domain (set notation): f. Range (set notation):

5. Given the graph, draw the asymptotes as dotted line, write the equation and identify the asymptotes, Domain & Range. a. Equation: b. Vertical Asymptote: c. Horizontal Asymptote: d. y-intercept: e. Domain (set notation): f. Range (set notation):

6. Write a rational function in the form of 𝑓𝑓(𝑥𝑥) = • • •

Double zero (double roots) at x = 5 Hole at x = 2 Vertical asymptotes at x = 0 and x = -3

Horizontal asymptotes at y =

−4 5

𝑝𝑝(𝑥𝑥) , 𝑞𝑞(𝑥𝑥)

with all the given characteristics:

7. Write a rational function in the form of 𝑓𝑓(𝑥𝑥) = Zero at x = -4 Hole at x = 3 Vertical asymptotes at x = 1 and x = -5

• • •

Horizontal asymptotes at y =

𝑝𝑝(𝑥𝑥) , 𝑞𝑞(𝑥𝑥)

with all the given characteristics:

2 3

Problems 8 and 9, sketch the functions. (Note: don’t use the calculator for sketch). Identify main attributes as you have done in previous problems.

(Show all your factoring work here and identify each attributes) Describe the Domain using both Interval and Set-Builder Notations.

10) The graph of the function f is shown on the grid below. y

Based on the graph, for what values of x is f(x) > 2?

6

5

4 3

2

1 x −4

−3

−2

−1

1 −1 −2

−3

−4

−5

2

3

4

5

6

7

8

Based on the graph, for what values of x is f(x) > 0?