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Chapter 0- Functions and Precalculus
TEST REVIEW
Important Topics:
Interval Notation/Set Notation, Distance/Midpoint, Union/Intersection, Function, Domain/Range,
Local/Global Max, Local/Global Min, Inflection Point, Concave Up/Down,
Positive/Negative/Increasing/Decreasing, Average Rate of Change, Piecewise Function, Slope-Intercept
Form, Absolute Value Function, Inverse, Odd/Even, Transformations
1. Simplify the expressions as much as possible. State the values where x is not defined.
Example:
9a 2  16
3a 2  a  4
2
1
1

 2
x2 x2 x 4
2. Find the domain of each function shown below and express it in interval notation.
Example:
x2
x  x6
2
x 3
1 x
x2
x
3. Solve the following. Write solutions to inequalities in interval notation.
Example: 2 x 2  5 x  3  0
2 x  y  4

3x  2 y
Example: x3  x  0
x 2  7 x  10
0
4 x2  6 x  2
2 x2  5x  3
3x  y 2  3
 y 1  x
Example: 
6 x 2  x3  9 x
x 1
0
x2
4. Write the solution to the following absolute value function in interval notation:
Example: |3x-4| < 5
|7 – 4x| < 11
5. Determine if the points are on the graph of the function f ( x)  x 2  1  x3 .
Example: (1, 1)
(0, 1)
(1, 0)
6. Use a graphing calculator to help you find the domain and range of the following function
Example: f ( x) 
f ( x) 
5
3
x  16
2
1
5
x 4
2
7. For the piecewise function below, calculate f(-2), f(0), f(0.5) and f(3).
3 x  1 if x  0

if 0  x  1
4
 x3
if x  1

f(-2)
f(0)
f(0.5)
f(3)
8. Use the function to the right to find:
a.) Use interval notation to describe where the graph is
increasing.
b.) Use interval notation to describe where the graph is
decreasing.
c.) Use interval notation to describe where the graph is
positive.
d.) Use interval notation to describe where the graph is
negative.
e.) Use interval notation to describe where the graph is
concave up.
f.) Use interval notation to describe where the graph is
concave down.
9. Write an equation for a linear function whose graph has a slope of 3 and passes through the
point (2, 7)
10. Write an equation for a linear function whose graph passes through the points (1, 2) and
(4,6).
11. Given the f is an invertible function, fill in the blanks.
If f(2) = 5, then f-1(5) = __________.
If f-1(0) = -1, then f(-1) = __________.
If (3, 6) is on the graph of f, then __________ is on the graph of f--1.
12. Given that f ( x)  x and g ( x)  4 x 2 ,
find the domain of f(x) and g(x)
Example: find an equation and the domain for ( g f )( x)
find an equation and the domain for ( f g )( x)
13. Find the inverse of:
Example: f ( x)  4 x  2
f ( x) 
1
3
x2
14. Write the following as a piecewise function:
Example: g(x) = |2x+6|
h(x) = |4x + 7|
15. Suppose the point (8, -5) is on the graph of f(x).
Find a point on the graph of 2f(x)
____________________
Find a point on the graph of f(2x)
_____________________
Find a point on the graph of f(x) – 3 _____________________
Find a point on the graph of f(x+7) + 10
____________________
If f(x) is symmetric over the y-axis (“EVEN”), find another point on f(x) ____________________
Ex.
If f(x) is has rotational symmetry (“ODD”), find another point on f(x) ____________________
Ex.
19. Describe the transformation from y = x2 to the following graphs.
Example: y  4  2( x  1)2
y  5  3( x  2)2
20. Find the average rate of change of the function:
Example: f(x) = 2x-1 over the interval [-2, 0]
f(x) = 3x2 – 7 over the interval [-3, 1]
p.91: 3, 7, 9, 11, 13, 19, 21, 25, 27, 33