Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
106
© 2014 Pacific Crest
Step
Explanation
Watch it Work!
8.
Determine if
the function is
increasing or
decreasing
An important feature of a function is
when it is increasing and when it is
decreasing.
The function is always decreasing.
9.
Determine
function’s end
behavior
Determine what the behavior of the
function is when its domain values
approach –∞ or +∞.
The function approaches
0 as
x
gets large.
10. Validate your
analysis
Compare your analysis against the
family of function cards available
at the companion website. You can
validate your graph through the use of
a graphing calculator.
The analysis fits the Rational
family of functions card, within the
constraints of
x
> 0.
Scenario:
Analyze the function:
h
(
t
) =
t
2
– 5
t
– 6
Step
Watch it Work!
1.
Convert to function notation
Already in function notation
2.
Determine the function’s family
This is a quadratic function.
3.
Determine the domain
The domain is all real numbers.
4.
Graph the function
-6
y
1
-12
t
h(t)
=
t
2
– 5
t
– 6
-1
5.
Asymptotes
Quadratic functions have no asymptotes.
6.
Determine the range of the function
From the graph, the range is [–12.25, ∞)
Note that the minimum occurs when
2.5
2
b t
a
−
= =
h
(2.5) = –12.25