Section 1.5

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Section 1.5 Properties of Functions Library of
Functions
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A function f is increasing on an open interval I
if, for any choice of x1 and x2 in I, with x1 lt
x2, we have f(x1) lt f(x2).
A function f is decreasing on an open interval I
if, for any choice of x1 and x2 in I, with x1 lt
x2, we have f(x1) gt f(x2).
A function f is constant on an open interval I
if, for any choice of x in I, the values of f(x)
are equal.
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Increasing (0,2)
0 lt x lt 2
y
Decreasing (2,7)
2 lt x lt 7
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(2, 3)
Constant (7,10)
7 lt x lt 10
(4, 0)
0
(1, 0)
x
(10, -3)
(0, -3)
(7, -3)
-4
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A function f has a local maximum at c if there is
an interval I containing c so that, for all x in
I, f(x) lt f(c). We call f(c) a local maximum of
f.
A function f has a local minimum at c if there is
an interval I containing c so that, for all x in
I, f(x) gt f(c). We call f(c) a local minimum of
f.
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Symmetry examples
g(-z) -(-z)22 -z22
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A linear function is a function of the form
f(x)mxb
The graph of a linear function is a line with a
slope m and y-intercept b.
(0,b)
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A constant function is a function of the form
f(x)b
y
b
x
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Identity function is a function of a form
f(x)x
(1,1)
(0,0)
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The square function
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Cube Function
(1,1)
(-1,-1)
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Square Root Function
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Reciprocal Function
(1,1)
(-1,-1)
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Absolute Value Function
(1,1)
(-1,1)
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(1, 3)
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Section 1.6 Graphing Techniques Transformations
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Graph the function
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(2, 4)
(0, 0)
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(2, 4)
(-1, 4)
(-3, 0)
(0, 0)
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(-1, 6)
(-1, 4)
(2, 4)
(-3, 2)
(0, 0)
(-3, 0)
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(4, 2)
(0, 0)
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(4, 2)
(8, 2)
(0, 0)
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(8, 6)
(4, 2)
(8, 2)
(0, 0)
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(9, 3)
(0, 0)
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(-9, 3)
(9, 3)
(0, 0)
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(-9, 3)
(9, 3)
(0, 0)
(-9, -3)