7.3 Power Functions

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7.3 Power Functions Function Operations

• p. 415

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Sum f(x) g(x) (fg)(x)
Difference f(x) - g(x) (f-g)(x)
Product f(x) g(x) (fg)(x)
Quotient
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f(x) 2x 3 and g(x)
Sum
Difference
Product
Quotient
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Functions
In order for a relationship to be a function
EVERY INPUT MUST HAVE AN OUTPUT
TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT
ONE INPUT CAN HAVE ONLY ONE OUTPUT
INPUT
(DOMAIN)
FUNCTIONMACHINE
OUTPUT
(RANGE)
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Look on page 67

• No two ordered pairs can have the same first
  coordinate
• (and different second coordinates).

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Time of Day
Degrees C
15
3
1
6
2
4
9
1
4
11
12
7
6
13
2
5
10
3
8
5
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Domain Inputs 1,2,3,4,5,6
Contains the Range Outputs 9,10,12,13,15
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Ex.
Is this a function?
(2,5) , (3,8) , (4,6) , (7, 20)
(1,4) , (1,5) , (2,3) , (9, 28)
(1,0) , (4,0) , (9,0) , (21, 0)
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Notation
f of x
Input x Output f(x) y
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Ex Let f(x)3x1/3 g(x)2x1/3. Find (a) the
sum, (b) the difference, and (c) the domain for
each.

• 3x1/3 2x1/3
• 5x1/3
• 3x1/3 2x1/3
• x1/3
• Domain of (a) all real numbers
• Domain of (b) all real numbers

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Ex Let f(x)4x1/3 g(x)x1/2. Find (a) the
product, (b) the quotient, and (c) the domain for
each.

• 4x1/3 x1/2 4x1/31/2 4x5/6
• 4x1/3-1/2
• 4x-1/6

(c) Domain of (a) all reals 0, because you
cant take the 6th root of a negative number.
Domain of (b) all reals gt 0, because you cant
take the 6th root of a negative number and you
cant have a denominator of zero.
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Evaluate (f-g)(x) when x 2 for the functions
(f - g)(x)
(f - g)(2)
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Composition

• f(g(x)) means you take the function g and plug
  it in for the x-values in the function f, then
  simplify.
• g(f(x)) means you take the function f and plug
  it in for the x-values in the function g, then
  simplify.

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The COMPOSITION of the function f with g is
Plug the second function into the first
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Evaluate the following when x 0, 1, 2, 3 given
that
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Ex Let f(x)2x-1 g(x)x2-1. Find (a)
f(g(x)), (b) g(f(x)), (c) f(f(x)), and (d) the
domain of each.

• (a) 2(x2-1)-1

(c) 2(2x-1)-1 2(2-1x)
(b) (2x-1)2-1 22x-2-1
(d) Domain of (a) all reals except x1. Domain
of (b) all reals except x0. Domain of (c) all
reals except x0, because 2x-1 cant have x0.
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Journal

• When I hear someone say Math is Fun I
• 5 sentences minimum

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Assignment
418-419/12-48 mult. of 3