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© 2014 Pacific Crest
107
Step
Watch it Work!
7.
Determine the function’s intercepts
The
y
-intercept (0, –6) occurs when
t
= 0.
Solve 0 =
t
2
– 5
t
– 6 to find the t-intercepts.
0 = (
t
– 6)(
t
+ 1), so
t
= 6 or
t
= –1.
The
t
-intercepts are (6, 0) and (–1, 0).
8.
Determine if the function is
increasing or decreasing
The function is decreasing on the interval
(–∞, 2.5) and increasing on the interval (2.5, ∞).
9.
Determine function’s end behavior
The function goes to ∞ as
x
gets large (positive)
and as
x
gets very small (negative).
10. Validate your analysis
The analysis fits the Quadratic family of functions card,
with a range of [-12.25, ∞).
YOUR
TURN!
Scenario:
Analyze the function: ( ) 3 2
x
g x
=
x
> 0.
O
ops
! A
voiding
C
ommon
E
rrors
●
Missing key behavioral characteristics of a function
Example
: Analyze
the function
2
1
( )
1
g x
x
=
+
The graph increases from –
∞
to 0
and decreases from 0 to
∞
with a
y
-intercept at (0, 1).
Why?
The function has a horizontal asymptote at
y
= 0 with the function values approaching
0 through positive range values as |
x
|
→
∞
. The information about increasing and
decreasing is correct in the example, as is the
y
-intercept.
2.5 Analyzing a Function