Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
112
© 2014 Pacific Crest
Scenario C:
Analyze the function:
x
2
y
+
x
= 4
Step
Model
1.
Convert to function notation
2
2
2
2
4
4
4
4 ( )
x y x
x y
x
x
y
x
x
f x
x
+ =
= −
−
=
−
=
2.
Determine the function’s family
Rational function
3.
Determine the domain of the function
All real numbers except
x
= 0
4.
Graph the function
5.
Asymptotes
x
= 0
6.
Determine the range of the function
1
1
,
where
0.0625
16
16
− +∞
− = −
7.
Determine the function’s intercepts
Intercepts:
x
-intercept at (4,0).
There is no
x
-intercept.
8.
Determine if the function is increasing
or decreasing
Increasing from –∞ to 0 and from 8 to ∞.
Decreasing from 0 to 8.
9.
Determine function’s end behavior
The graph is decreasing to 0 through positive values as
–∞ ←
x
. The graph is increasing to 0 through negative
values as
x
→ ∞. The graph is unbounded.
10. Validate your analysis
The function graph should behave like
2
1 ( )
g x
x
=
Check against the function card
for the family of rational functions.