Precalculus
Chapter 1 Test Review 1. Determine which of the following relations represents a function.
Name__________________
A = {(0, 1), (2, 1), (3, 4)}
2. Given f ( x ) = 10 3 x , find f (2) .
B = {(2, 1), (2, 1), (0, 4)}
C = {(2, 1), (2, 1), (3, 4)}
3x + 7, x < 3 , find f (4) . 3. Given f (x ) = 2 4x 1, x 3
4. Find the domain of the function A. f (x ) = x 2 + 5x + 6 5. If f (x ) = 2x 3 , find B. f (x ) = 3 x
f (x + h ) f (x ) , h 0. h
6. An open box is to be made from a square piece of material 12 inches on a side by cutting equal squares from each corner and turning up the sides. Write the volume V of the box as a function of x . What is the domain of the function?
12 - 2x
x 12 - 2x x
7. Determine the function of the graph below.
4
-5
-2
-4
8. Determine the open intervals on which the function is increasing, decreasing, or constant. A. f (x ) = 2x 6 + 5x 4 x 2 B. f (x ) = 4x 3 x C. f (x ) = x + 5
9. Is the following function even, odd or neither? A. f (x ) = 2x 6 + 5x 4 x 2 B. f (x ) = 4x 3 x C. f (x ) = x + 5
10. Write the height of the rectangle as a function of x.
f ( x) =
2
(HINT: h = Top Bottom )
x 2 -2
-2
-1
g ( x ) = -x
-2
Precalculus Ch1 Review.doc
11. Approximate any relative maxima or minima. A. f (x ) = x 3 5x 2 + 12 B. f (x ) = x 5 x 3 + 2
12. A wire 100 inches long is to be cut into four pieces to form a rectangle with one side that has a length of x. Express the area A of the rectangle as a function of x. Determine the domain of the function and approximate the maximum area of the rectangle. 13. Identify the common function and describe the transformation of the graph. A. g (x ) = 2(x 5)3 + 3 B. g (x ) = x 7 + 7 C. g (x ) = 4 x 7 D. g (x ) = (x 3)2 + 5
14. Describe the graph of g (x ) = f (x + 2) relative to f (x ) . 15. Given f (x ) = x 2 and g (x ) = 2 x , find (f g )(x ) . 16. Given f (x ) = x 2 and g (x ) = 2 x , find (fg )(x ) . 17. Given f (x ) = x 2 and g (x ) = 2 x , find (f + g )( 2) . 18. Given f (x ) = x 2 and g (x ) = 2 x , find (f g )( 1) . 19. Given f (x ) = x 2 and g (x ) = 2 x , find (f 20. Find two functions f and g, such that A. (f
g )(x ) .
g )(x ) = (x + 12)2
B. (f
g )(x ) =
1 (3x 1)
21. Determine if the functions f (x ) = 2x + 4 and g (x ) =
1 x 4 are inverses of each other. 2
22. Determine algebraically which functions are one-to-one. A. f (x ) = x 3 + 8 23. Find f
1
B. f (x ) = x 2 3 + 6
C. f (x ) =
3x x 8
(x ) , if possible.
B. f (x ) = x 2 3 + 6 C. f (x ) =
A. f (x ) = x 3 + 8
3x x 8
24. Given f (x ) = 5x + 2 and g (x ) =
2x , find (f 3
g 1 )(1) .
