CCF - Operations with Functions (Lesson)
Operations with Functions
Recall that a relation is any set of ordered pairs. A function is a set of ordered pairs in which each x-value maps to exactly one y-value.
Function or Not a Function Practice
- {(3, -1) (5, -1) (7, -1) (9, -1)}
- {(2, 3) (3, -1) (5, 6) (-2, 4)}
- {(9, 1) (-8, 2) (3, 6) (10, 1}
- {(3, 5) (3, 2) (3, 1) (3, 7)}
- {(2, -1) (5, -1) (5, 6) (-1, 2)}
- {(-7, 8) (8, 9) (9, -7) (-7, 10)}
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
A function takes an input, the domain, and gives you an output, the range.
|
x |
f(x) = 3x + 2 |
(x, f(x)) |
|---|---|---|
|
-3 |
f(-3) = 3(-3) + 2 = -9 + 2 = -7 |
(-3, -7) |
|
-2 |
f(-2) = 3(-2) + 2 = -6 + 2 = -4 |
(-2, -4) |
|
-1 |
f(-1) = 3(-1) + 2 = -3 + 2 = -1 |
(-1, -1) |
|
0 |
f(0) = 3(0) +2 = 0 + 2 = 2 |
(0, 2) |
|
1 |
f(1) = 3(1) + 2 = 3 + 2 = 5 |
(1, 5) |
|
2 |
f(2) = 3 (2) + 2 = 6 + 2 = 8 |
(2, 8) |
|
3 |
f(3) = 3(3) + 2 = 9 + 2 = 11 |
(3, 11) |
Evaluate the Following Functions Practice
Evaluate the following functions for the given value of x:
1. For f(x) = -2x + 5, find f(7).
2. For h(x) = 3x2 + 1, find h(2).
3. For g(x) = 2x + 3, find g(3).
4. For f(x) = -x + 7, find f(11).
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
Now, we want to practice making new functions through operations with functions - but first let us make sure we understand the notation:
|
Operation |
Notation #1 |
Notation #2 |
Example f(x) = 3x + 2 g(x) = x2 + 3x - 7 |
|
Addition |
f(x) + g(x) |
(f + g)(x) |
f(x) + g(x) = 3x + 2 + x2+ 3x - 7 = x2 +6x - 5 |
|---|---|---|---|
|
Subtraction |
f(x) - g(x) |
(f - g)(x) |
f(x) - g(x) = 3x + 2 - (x2+ 3x - 7) = 3x + 2 - x2 - 3x + 7 = -x2 + 9 |
|
Multiplication |
f(x) |
(f |
f(x) (3x + 2)(x2 +3x - 7) = 3x3 + 9x2 - 21x + 2x2 + 6x -14 3x3 + 11x2 -15x -14 |
Watch this video to try a few more:
Given f(x) and g(x) Practice
Given f(x) = 5x + 1 and g(x) = 2x2 - 3x + 1, find the following:
- g(x) - f(x)
- (f+g)(2)
- f(3) - g(-1)
- (f
⋅ g)(x)
- (f
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
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