Combining Functions
Function Type
Given Inputs
Given Outputs
100
f(x) = x + 1 g(x) = x + 1
(f + g)(x)?
(f + g)(x) = 2x + 2
100
Linear, Quadratic, or Non-Polynomial?
Linear Polynomial Function
100
f(x) = x + 3
f(2) = ?
f(2) = 2 +3
f(2) = 5
100
f(x) = x + 3
What is x when f(x) is 8?
When f(x) = 8,
8 = x + 3
x = 5
200
f(x) = x + 1 g(x) = x + 2
(f + g)(x)?
(f + g)(x) = 2x + 3
200
Linear, Quadratic, or Non-Polynomial?
Quadratic Polynomial Function
200
f(x) = x + 5
f(5) = ?
f(5) = 5 + 5
f(5) = 10
200
f(x) = x + 5
What is x when f(x) = 10?
When f(x) = 10,
10 = x + 5
x = 5
300
f(x) = x + 3 g(x) = x + 5
(f + g)(x)?
(f + g)(x) = 2x + 8
300
Linear, Quadratic, or Non-Polynomial Function?
Non-Polynomial Function
300
f(x) = 2x
f(3) = ?
f(3) = 2(3)
f(3) = 6
300
f(x) = 2x
What is x when f(x) = 10?
When f(x) = 10,
10 = 2x
x = 5
400
f(x) = 2x + 3 g(x) = x + 1
(f + g)(x)?
(f + g)(x) = 3x + 4
400
3x + 2
Linear, Quadratic, or Non-Polynomial Function?
Linear Function
400
f(x) = 2x + 1
f(2) = ?
f(2) = 2(2) +1
f(2) = 4 +1
f(2) = 5
400
f(x) = 2x + 1
What is x when f(x) is 11?
When f(x) = 11,
11 = 2x + 1
10 = 2x
x = 5
500
f(x) = 2x + 5 g(x) = x -1
(f + g)(x)?
(f + g)(x) = 3x + 4
500
x2 + 5x + 6
Linear, Quadratic, or Non-Polynomial Function?
Quadratic Function
500
(f + g)(x) = 3x + 6
(f + g)(10) = ?
(f + g)(x) = 3(10) + 6
(f + g)(x) = 30 + 6
(f + g)(x) = 36
500
(f + g)(x) = 3x + 6
What is x when (f + g)(x) = 21?
When (f + g)(x) = 21,
21 = 3x + 6
15 = 3x
X = 5