Algebra 2Name:______

Function Test Review

Vocab You Should Know:Domain, Range, Relation, Function, Vertical Line Test, Composition, Inverse, Horizontal Line Test

Find the domain and range of each relation, then determine if the relation is a function.

1. {(-2, -2), (-1, -1), (1, 1), (2, 2)}2. {(4, 2), (4, -2), (9, 3), (9, -3)}

D: ______D: ______

R: ______R: ______

Function? Yes or NoFunction? Yes or No

3.4.5.

D: ______D: ______D: ______

R: ______R: ______R: ______

Function? Yes or NoFunction? Yes or NoFunction? Yes or No


Remember! There are two conditions under which a function cannot exist:

  1. x in the denominator: denominator can never equal 0
  1. square root sign: whatever is under the square root MUST be greater than or equal to 0

Otherwise, the domain is all reals.

Determine the domain of each function.

6) f(x) = 5x – 1

D: ______

7) g(x) =

D: ______

9) d(x) =

D: ______

10)h(x) =

D: ______

11) a(x) =

D: ______

12) c(x) =

D: ______

13) w(x) =

D: ______

14) q(x) =

D: ______

Evaluate each function for the given values of x:

15. a. f(3) = ______b. f(-2) = ______

16. a. f(-3) = ______b. f(0) = ______

Let f(x) = and . Evaluate each function.

17. f(6) = ______18. g(1) = ______

19. f(1) + g(0) = ______20. g(4) – f(5) = ______

Operations with Functions: add, subtract, multiply, divide

Let and . Find the following:

21. = ______22. = ______

23. = ______24. = ______

25. = ______26. = ______

27. = ______28. = ______

domain restriction? ______

Composition of Functions:

Let f and g be functions of x.

The composition of f with gis defined by .

You plug the second function into the first function!

29. Let and . Find the following composite functions.

a. Find .b. Find .

c. Find .d. Find .

30. Let and . Find the following.

a. b.

c. d.

Inverse Functions

The domain of the inverse is the ______of the original function.

The range of the inverse is the ______of the original function.

The graph of a function and its inverse are reflected over the line ______.

State if the relation is a function. Find the inverse of each relation. State if the inverse is a function.

31. {(1, 0), (-2, 3), (3, -6), (4, -6)}32. {(0, 0), (-1, 6), (0, 6), (3, 9)}

Function? Yes or NoFunction? Yes or No

Inverse: ______Inverse: ______

Is the inverse a function? Yes or No Is the inverse a function? Yes or No

Find the equation of the inverse of each function.

33. 34.

35. 36.

Find the equation of the inverse of each function. Then, use composition to verify that the equation you wrote is the inverse.

Follow the same process every time. Keep your work NEAT!

37.

38.

Absolute Value Transformations
If y = a|x – h| + k, a stretches or shrinks the graph of y = |x – h| + k.
If |a| > 1, the graph is vertically stretched.
If |a| < 1, the graph is vertically shrunk.
If a is negative, the graph is turned upside down.

39. Graph the absolute value equation.

f(x) = 3|x – 2| – 1

Vertex:

Horizontal Shift:

Vertical Shift:

Opens up/down?

Stretched/Shrunk/Same?

40. Graph the absolute value equation by hand.

f(x) = -|x + 4| + 2

Vertex:

Horizontal shift:

Vertical Shift:

Opens up/down?

Stretched/Shrunk/Same?

41. Graph the absolute value equation by hand.

f(x) = ½|x + 3|

Vertex:

Horizontal shift:

Vertical Shift:

Opens up/down?

Stretched/Shrunk/Same?