2.3
ANALYZING GRAPHS OF FUNCTIONS
The graph of a function is the collection of points x, y  where
x  the directed distance from the y-axis.
y  the directed distance from the x-axis.
y  f x  .
Example 1. The domain and range of a function.
Find the domain and range of the function. Then find f  1, f 0, f 1, f 2 .
Example 2. Use the Vertical Line Test to decide whether the graphs represent a
function.
Example 3. Find the zeros of the following functions:
A) f x   3x2  x  10
B) g x   10  x 2
C)
ht  
2t  3
t 5
INCREASING AND DECREASING FUNCTIONS
Example 4. Describe the increasing or decreasing behavior of each function
shown.
A) f x   x
3
B) f x   x  3x
3
t  1,
C) f t   1,
 t  3,

if t  0
if 0  t  2
if t  2
Relative Minimum, Relative Maximum (also called Local Minimum, Local
Maximum)
Example 5
Use a graphing utility to approximate the relative minimum of the function given
by f x   3x 2  4 x  2 .
Information from the Graph of a Function
A function can be evaluated by using its graph. Use the graph on the next page to evaluate f(-4), f(-1),
f(0), f(1), f(2). Then find the domain and range of the function. Give the interval over which the
function is increasing, decreasing, and constant. Finally, give all x values for which f(x) = 1.
4
3
2
1
-6
-4
-2
2
-1
-2
-3
-4
4
6