Pre-Calc Practice Test: Chapter 1
Name_________________________
1. Define each of the terms.
a. Relation
b. Domain
d. Function
c. Range
e. One-to-One Function
In questions 2-4 use the function g ( x) = x 2 + 3 x .
2. g(4)
3. g(-2)
4. g(x - 3)
Graph y = x3 − 4 x on your graphing calculator and use it to answer questions 5-7.
5. Indicate the intervals
6. List the relative
7. Show a small sketch of
where the function is
minimum and the relative
the graph and explain if it is
increasing and/or
maximum for the function
odd, even, or neither
decreasing.
In questions 8-10, list the domain and range of each graph.
8.
9.
10.
In questions 11-13, use the function
11. Find f(2)
f ( x) =
12. Find f(-1)
2 x + 1, x ≤ 0
.
x>0
4
13. Find f(0)
In questions 14-16, use the functions f ( x ) = 2 x + 3 and g ( x ) = x 2 + 1 .
14. Find (f + g)(x)
15. Find (f/g)(x)
16. Find g(f(x))
In questions 17 and 18, use the functions f ( x ) = 1 − x 2 and g ( x ) = 1 − x .
17. Find f(g(x))
18. Find g(f(x))
In questions 19-21, find the inverse of each function below if it is one-to-one. If the
function is not one-to-one simply state that.
20. g ( x ) = − x + 2
21. h ( x ) = x3
19. f ( x ) = 2 x + 3
In questions 22 & 23, use composites to tell if the functions below are inverses or
not. Show All Work.
1
1
3
23. f ( x ) = x 3 − 4 & g ( x ) = 3 x + 4
22. f ( x ) = x − & g ( x ) = ( 2 x + 1)
3
2
2
In questions 24 & 25, are the relations below functions? Explain or show why.
25. y = 2 x + 1
24. x 2 + y 2 = 16