32
CHAPTER 1
Functions and Limits
Table 3 Families of Essential Functions and Their Graphs
Linear
Functions
y
y
f sxd − mx 1 b
b
b
x
0
Power
Functions
b
x
0
ƒ=b
ƒ=mx+b
y
y
y
y
f sxd − x n
x
0
x
0
ƒ=≈
Root
Functions
0
x
x
0
ƒ=˛
ƒ=x$
ƒ=x%
y
y
y
y
n
f sxd − s
x
x
0
Reciprocal
Functions
f sxd −
1
xn
0
x
x
$x
ƒ=œ„
%x
ƒ=œ„
y
y
y
y
x
0
1
x
0
0
x
1
ƒ=
≈
y
0
x
1
ƒ=
x$
y
0
1
x
1
ƒ=
˛
y
x
1
1
x
0
ƒ=b® (b>1)
Trigonometric
Functions
0
ƒ=Œ„
x
f sxd − b x
f sxd − log b x
x
ƒ= œ„
x
ƒ=
Exponential
and Logarithmic
Functions
0
0
x
ƒ=b® (b<1)
y
1
ƒ=log b x (b>1)
y
y
1
f sxd − sin x
f sxd − cos x
f sxd − tan x
0
ƒ=sin x
π
2π x
0
ƒ=cos x
π
2π
x
_
π
2
0
π
2
x
ƒ=tan x
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