Pre-Calculus Chapter 1 Review

1. Chapter 1 Review

2. Use the quadratic formula to find the exact solution.
2
x 15 3x
3 69
a.) x
2
b.) x 3 51
2
c.) x 3 69
2
1 181
d.) x 2

3. Solve for x.
a.) x 14
b.) x 196
c.) x 14
d.) x 12.25

4. Solve for y.
2y2 + 4 = 9y
a.) y = 1/2 and y = 2
b.) y = 2
c.) y = 2 and y = 1
d.) y = 1/2 and y = 4

5. Solve the Equation.
29 11
a.) y ,
9 8
b.) y 20,3
29 11
c.) y ,
9 8
9 8
d.) y ,
20 11

6. Solve the equation.-D
a.) x = 21, -21
b.) x = 0, 1
c.) x = 1, 3
d.) x = 1, -3

7. Solve the equation.
a.) x = -10, x = 1
b.) x = -10, x = 8
c.) x = 10, x = 8
d.) x = 10, x = -8

8. Find the domain and range of the function.
Write your answers using interval notation.

9. Find the domain and range of the function.
Write your answers using interval notation.

10. Find the domain and range of the function.
Write your answers using interval notation.
y = –x4 + 4
3

11. Find the asymptotes in the following equation.

12. Determine if the following function
is continuous at x = -2 .

13. For what values of x is the
function discontinuous?

14. For what values of x is the
function continuous?

15. Determine the intervals on which the function is
increasing, decreasing, and constant.

16. Determine the intervals on which the function is
increasing, decreasing, and constant.

17. Which function is decreasing over its entirety?
a.) b.)
c.) d.)

18. Give the function’s boundedness.
a.) bounded
b.) upper bound
c.) lower bound
d.) unbound

19. Give the function’s boundedness.
a.) bounded
b.) upper bound
c.) lower bound
d.) unbound

20. Graph the following piecewise function.
Is it continuous at x = 0?

21. Identify local and absolute extrema in the
following functions.
1.) f(x) = -x2 - 12x - 42
2.) f(x) = x3 – 3x

22. Is the function even, odd, or neither?
1.) f(x) = 6x5 – 4x3
a.) even b.) odd c.) neither
2.) f(x) = 10x - 5x
a.) even b.) odd c.) neither
3.) f(x) = x2 + 28
a.) even b.) odd c.) neither

23. Find fg and f/g. State the domain for each.
2
1. f (x) x 3; g(x) x
3
2. f (x) x ; g(x) x 4

24. Find f(g(2)) and g(f(-1)).
2
1. f (x) x 3; g(x) x
3
2. f (x) x ; g(x) x 3

25. Find f-1(x) of the following function.
State its domain.
3
1.) f (x) x 8
3x 2
2.) f (x)
x 1

26. How can the graph of f(x) =1/2(x + 11)2 - 8 be
obtained from the graph of y = x2?

27. How can the graph of f(x) = -10x3 + 3 be
obtained from the graph of y = x3?

28. Write the equation:
The shape of y = x is shifted 8 units to the left.
Then the graph is shifted 5 units upward.