Unit NineAlgebra II Practice TestRational Equations & Functions

Name______Period_____Date______

NON-CALCULATOR SECTION

Vocabulary: Define each word and give an example.

  1. Direct Variation
  1. Local Minimum
  1. Rational Function

Short Answer:

  1. Write the factoring pattern for the sum of two cubes.
  1. Describe how to find the horizontal asymptote(s) of a rational function.

Review:

  1. Find an equation for the inverse of the function:
  1. Write an equation in standard form for the line perpendicular to that passes through the point .
  1. Solve the equation:
  1. Simplify the expression:

Problems:

**Be sure to show all work used to obtain your answer. Circle or box in the final answer.**

  1. Identify the domain and range, the horizontal and vertical asymptote(s), local extrema (maxima or minima), and the x- and y- intercepts of the graph of the function. Then graph the function.

a. b.

Domain: ______Domain: ______

Range: ______Range: ______

Horizontal:______Horizontal: ______

Vertical: ______Vertical: ______

x-int: ______x-int: ______

y-int: ______y-int: ______

Local Extrema: ______Local Extrema: ______

  1. Simplify the expression.

a. b.

  1. Perform the indicated operation. Simplify your answers.

a. b.

c. d.

e. f.

g. h.

i. j.

Multiple Choice Section: Circle the correct answer.

  1. The value of w varies directly with x and inversely with y. If when and , what is the value of w when and ?
  1. Which of the following functions have an asymptote at ?
  1. II only
  2. I and II only
  3. I and III only
  4. I, II, and III
  1. What is the solution set of ?
  1. Which best describes all asymptotes of the function ?

A.x = 1, x = 2

B.x = 2, y = 0

C.x = 2, y = 1

D.x = 2, y = x

Name: ______Period______Date______

CALCULATOR SECTION

  1. Solve the rational equation. You may use your calculator to check your answers only.

a. b.

c. d.

  1. The intensity, I, of light received from a source varies inversely as the square of the distance, d, from the source. If the light intensity is 2 foot-candles at 12 feet, find the light intensity at 14 feet. Round your answer to the nearest hundredth if necessary.
  1. The variables x and y vary inversely, and when . Find an equation that relates the variables. What is the constant of variation?
  1. The variable z varies jointly with the product of x and y, and when and . Find an equation that relates the variables.
  1. You start a small t-shirt business, spending $750 for equipment. You figure it will cost $5.25 per t-shirt to create. How many t-shirts must you produce before your average cost per t-shirt is $6.00?
  1. What is the local maximum of the function ?

A.

B.

C.

D.

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