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Algebra 2 – Sec. 8.3 Guided Notes
“The Algebra of Functions”
Objectives:
1. Find the domain of a function.
2. Use the algebra of functions to combine functions and determine domains.
Domain of a function
STEPS:
1. For most functions it will be all real numbers.
2. However, when there is a x in denominator of a fraction or under a radical there are limits
that are place on the domain.
Example 1: Find the domain.
a. F (x) = 3x + 2
b. g (x) =
c. h(x) = √
Check Point 1: Find the domain.
a. F(x) = 5x – 6
c. h(x) = √
b. g(x) =
Algebra 2 – Sec. 8.3 Guided Notes
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Using the Algebra of functions
Example 2 let f(x)= x2 – 3, and g(x) = 4x + 5
a. ( f + g) (x)
b. (f + g) (3)
Check Point 2 let f(x) = 3x2 + 4x -1 and g(x) = 2x + 7
a. ( f + g) (x)
Example 3
b. (f + g) (4)
let f(x) = and g(x) =
a. (f – g)(x)
Algebra 2 – Sec. 8.3 Guided Notes
b. the domain of f – g
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Check point 3, let f(x)= and g(x) =
a. (f – g) (x)
b. the domain of f-g
Example 4. Let f(x) = x2 + x and g(x) = x – 5
a. (f + g)(4)
c. (f – g) (-3)
b. (fg)(x) and (fg)(-2)
Algebra 2 – Sec. 8.3 Guided Notes
d. ( )(x) and ( ) (7)
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Check Point 4.
a. (f + g) ( 5)
Let f(x) = x2 -2x and g(x) = x + 3
c. (fg) (-4)
b. (f – g) (-1)
Algebra 2 – Sec. 8.3 Guided Notes
d. ( ) (7)
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Algebra 2 – Sec. 8.3 Guided Notes
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Algebra 2 – Sec. 8.3 Guided Notes
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