GRAPHS OF PARENT FUNCTIONS
Linear Function Absolute Value Function Square Root Function
Domain: Domain: Domain:
Range: Range: Range:
x-intercept: Intercept: Intercept:
y-intercept: Decreasing on
Increasing on
Increasing when
Increasing on
Decreasing when
Even function
y-axis symmetry
Greatest Integer Function Quadratic (Squaring) Function Cubic Function
Domain: Domain: Domain:
Range: the set of integers Range : Range:
x-intercepts: in the interval Range : Intercept:
y-intercept: Intercept: Increasing on
Constant between each pair of Decreasing on for
Odd function
consecutive integers Increasing on for
Origin symmetry
Jumps vertically one unit at Increasing on for
each integer value Decreasing on for
Even function
y-axis symmetry
Relative minimum
relative maximum
or vertex:
共
0, 0
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a
<
0
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,
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a
>
0
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,
a
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0
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0,
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a
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0
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, 0
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a
>
0
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a
>
0
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,
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0, 0
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0, 0
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0, 0
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, 0
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a
<
0
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0, 1
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,
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0,
兲共
a
>
0
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,
兲共
,
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,
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x
(0, 0)
f(x) = x
3
−2 −3 1 2 3
−2
−1
−3
2
3
x
−1 −2 1 2 3 4
1
−1
−2
−3
2
3
f(x) = ax , a > 0
2
f(x) = ax , a < 0
2
x
1 −1 −2 −3 2 3
−3
1
2
3
f(x) = x
[[ ]]
f
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x
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x
3
f
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x
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ax
2
f
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x
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冀x冁
m
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m
>
0
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0,
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0, b
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b兾m, 0
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0,
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0,
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0,
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,
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x
−1 2 3 4
−1
1
2
3
4
(0, 0)
f(x) = x
x
−1 −2 2
−1
−2
1
2
(0, 0)
f(x) =
⏐
x
⏐
x
(0, b)
b
m
(
(
− , 0
b
m
(
(
− , 0
f(x) = mx + b,
m > 0
f(x) = mx + b,
m < 0
f
共
x
兲
冪
x
f
共
x
兲
ⱍ
x
ⱍ
冦
x,
x,
x
0
x
<
0
f
共
x
兲
mx b
9781133954316_FES.qxp 11/6/12 11:02 AM Page 2
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