Precalculus
Unit 1- Functions and Their Graphs
Name
Date
Tuesday August 25, 2015
Notes: Analyzing Graphs of Functions (Increasing, Decreasing, & Constant)
Determine if the graph is a function. Then identify the domain and range using interval notation.
1.
2.
3.
6
4
4
2
4
2
2
-5
5
5
-2
Function?
D:
R:
Function?
D:
R:
Function?
D:
R:
Increasing and Decreasing Functions
12
As you move from left to right, this graph decreases, then is constant, and then increases.
10
Increasing As you move left to right, the y-value gets larger
8
6
Decreasing As you move left to right, the y-value gets smaller
4
Constant As you move left to right, the y-value stays the same
2
b
5
1
HINT: the interval refers to the x-values the "word" refers to the y-values.
Use interval notation to determine intervals where the functions are increasing, decreasing and/or constant.
If the characteristic does not exist in the function, write none.
4.
5.
0.6
6.
2
2
0.4
5
0.2
-2
-0.5
0.5
-0.2
-4
-0.4
-2
-0.6
Increasing:
Decreasing:
Constant:
Increasing:
Decreasing:
Constant:
Increasing:
Decreasing:
Constant:
Sketch a graph of each function. Identify the domain and range and the intervals where each is increasing,
decreasing and/or constant. If the characteristic does not exist in the function, write none. Where indicated,
determine the intervals for which f ( x ) ≥ 0 .
f ( x) = x + 2 − 5
7.
Domain:
Range:
Increasing:
Decreasing:
Constant:
f ( x) ≥ 0 :
8.
f ( x) = − x − 4 + 1
Domain:
Range:
Increasing:
Decreasing:
Constant:
f ( x) ≥ 0 :
9.
f ( x) = x 2 − 4
Domain:
Range:
Increasing:
Decreasing:
Constant:
f ( x) ≥ 0 :
Local max/min
Absolute max/min
10.
a.) Given the graph of f ( x) , identify all local and absolute maximums and minimums.
Maximum
Minimum
Absolute
Local
b.) Then use the intervals given to identify if f ( x) > 0 or f ( x) < 0 .
( −∞, 1.3)
(1.3,
2.8 )
( 2.8, ∞ )