College AlgebraUnit 2 Review

2.1 Linear Equations in Two Variables

  1. Find the slope of a line containing the points and .
  1. Write an equation in slope-intercept form for a line passing through the points and .
  1. Write an equation for a line which passes through the point (2, -6) having a slope which is undefined.
  1. Write an equation for a line passing through the point that is parallel to the line .
  1. Write an equation for a line passing through the point that is perpendicular to the line .
  1. A small business buys a computer for $4,000. After 4 years, the value of the computer is expected to be $200. For accounting purposes, the business uses a linear depreciation model. Write a linear equation giving the value V of the equipment during the 4 years it will be in use.

2.2 Functions

  1. In the equation , is y a function of x? Explain how you know.
  1. In the equation , is y a function of x? Explain how you know.
  1. Given , a) find b) find .
  1. Given , find and .

Find the domain of the function. Write your answer as an inequality AND in interval notation.

11.12.

  1. For the function , find and simplify .
  1. A company has fixed costs of $95,000. It produces a product that costs $13.50 to make and sells for $35. Write a function that models this company’s profit when selling x number of this product.

The velocity of an object in motion is given by the function where v(t) is the velocity of the object in meters per second at time t.

  1. Find the velocity of the object after 25 seconds.
  1. After how many seconds does the object momentarily come to rest and then change directions?
  1. *A pediatrician wants to find a linear model that relates a child’s height, x, to head circumference, y. She randomly selects eight children from her practice, measures their height and head circumference, and obtains the data shown.

Height (in.) / 25 / 25.25 / 25.75 / 26.5 / 26.75 / 27 / 27.5 / 27.75
Head
Circumference (in) / 16.4 / 16.5 / 16.9 / 17.2 / 17.3 / 17.4 / 17.5 / 17.6
  1. Find and interpret the result in the context of the problem. (Round to two decimal places.)
  1. Find a linear model for the data algebraically. Use the point (25, 16.4).
  1. Use the linear model found in part b) to predict the height of a child with a head circumference measurement of 18 in.

2.3 Analyzing Functions of Functions

  1. In graph A below, is y a function of x? 19. In graph B above, is y a function of x?

Explain how you know.Explain how you know.

Find the zeros of the functions.

20.21.22.

23.Find the domain and range of the function in graph C shown here.

Give the interval(s) where the function is increasing, and the interval(s) where it is decreasing.

24.25.

Use an algebraic test to determine if is even, odd, or neither.

26.27.

28.Given that the point (-a, b) is on the graph of h(x), find the coordinates of another point on the graph if h(x) is even. What about if h(x) is odd?

2.4 Piecewise Functions

29.Draw a graph of the function

2.5 Transformations of Functions

  1. Given the graph of f(x) shown at right, sketch each of the following
  1. b.
  1. Write an equation for a function that has the shape of , but reflected in the x-axis, then moved left 5 units and down 3 units.
  1. Write an equation for a function that has the shape of , but reflected in the x-axis, then moved right 4 units and up 2 units.
  1. Find the domain and range of the function .
  1. Find the equation of function g(x)as shown.

2.6Combinations of Functions: Composite Functions

For problems #35-42, use the functions and . State the domain of the functions.

  1. Find and simplify .36. Find and simplify .
  1. Find and simplify .38. Find and simplify .

39. Find and simplify .40. Find and simplify .

  1. Find, simplify, and give the domain of .42. Find, simplify, and give the domain of .
  1. A raindrop hitting a pool of water creates concentric circles which grow increasingly large. Let represent the radius, r (in inches) of a circle t seconds after the raindrop lands. If the area, A of a circle is .

Find and interpret and .

2.7 Inverse Functions

  1. Given the function , find the formula for the inverse function .

For problems #45-46, suppose the number of rental units that are occupied is given by the function

, where p is the monthly rental price per unit.

  1. Find the inverse of D(p) and Describe the meaning of each variable.
  1. Find and interpret its meaning.

Answers to Exam Unit 2 Review - worked out solutions will be posted on web backpack

  1. Slope =
  2. x = 2

  1. Yes, for each x, there is exactly one y
  2. No, x could have more than one corresponding y. Ex.
  1. 4x + 2h – 1
  2. -1672 m/s
  3. after approximately 3.67 sec.
  4. a. 0.44; The circumference of a child’s head increases by approximately 0.44 inches for each 1 inch increase in height.

b.

c. 28.64 in.

  1. Yes, passes the Vertical Line Test
  2. No, does not pass the Vertical Line Test
  3. Domain:

Range:

  1. Increasing

Decreasing

  1. Increasing

Decreasing

  1. Thus f(x) is NEITHER
  2. Thus f(x) is EVEN
  3. (a, b) ifh(x) is EVEN

(a, -b) ifh(x) is ODD

a.

30

b.

  1. Domain ; Range

Domain

Domain

represents the area(in2) of a circle created by a raindrop t seconds after it lands

Three seconds after a raindrop lands, the area of the circle created is approximately 7.07 in2

represents the monthly rental price per unit when p units are occupied

When 60 units are occupied, the monthly rental price is $1,140.