Name________________________
Date ________
HW: Increasing and Decreasing Functions
I. REVIEW from Algebra I
For the function defined by
1. f(2)
4. f(-5)
f(x) = 3x2 – x + 1, Evaluate the following:
2. f(-2)
3.
5. f(
f(5)
1
)
2
II. PRACTICE (given a graph)
For each function below, state the domain and range, name the intervals where the
function is increasing or decreasing. Use the notation of your choice.
6.
7.
Domain
Domain
__________________
Range
Range
__________________
Increasing
Increasing
__________________
Decreasing
Decreasing __________________
8.
9.
Domain
Domain
__________________
Range
Range
__________________
Increasing
Increasing
__________________
Decreasing
Decreasing __________________
III. MORE PRACTICE (NEED a calculator )
For the following, graph the function using your calculator. List the appropriate intervals in
BOTH interval and inequality notation.
11. f (x) = x 2
10. f (x) = 3x + 5
y
y
x
x
Domain
Domain
__________________
Range
Range
__________________
Increasing
Increasing
__________________
Decreasing
Decreasing __________________
12. f (x) = (x + 3)2
13.
f (x) = − 2 x 2 − 2
y
y
x
x
Domain
Domain
__________________
Range
Range
__________________
Increasing
Increasing
__________________
Decreasing
Decreasing __________________
15. f ( x) = x − 1 + 3
14. f (x) = x 3 + 6 x 2 + 9 x
y
y
x
x
Domain
Domain
__________________
Range
Range
__________________
Increasing
Increasing
__________________
Decreasing
Decreasing ________________
16. State the domain and range for each of the following graphs. Then, state the
intervals where the function is increasing and where the function is decreasing.
a)
b)
Domain
Domain
__________________
Range
Range
__________________
Increasing
Increasing
__________________
Decreasing
Decreasing __________________
17.