Functions and Graphs
Function Notation
Example
For the function f(x) = 4x2 - 5x + 10, find:
a. f(3)
b. f(-2)
c. f(a)
Solution
a. To calculate f(3) means to find the value of the function when the
input variable has a value of 3. That is, substitute 3 for x and then
simplify:
| a. |
Original function.
Substitute 3 for x.
Multiply.
Add and subtract. |
f(x)
f(3) |
= 4x2 - 5x + 10 = 4(3)2
- 5(3) + 10
= 36 - 15 + 10
= 31 |
So, when x = 3, the value of the function is 31. That is, f(3) = 31.
This can be written as the ordered pair (3, 31).
| b. |
Original function.
Substitute -2 for x.
Multiply.
Add. |
f(x)
f(-2) |
= 4x2 - 5x + 10 = 4(-2)2
- 5(-2) + 10
= 16 + 10 + 10
= 36
|
So, when x = -2, the value of the function is 36. That is, f(-2) = 36.
This can be written as the ordered pair (-2, 36).
| c. |
Original function.
Substitute a for x.
Simplify. |
f(x)
f(a) |
= 4x2 - 5x + 10 = 4(a)2
- 5(a) + 10
= 4a2 - 5a + 10
|
Since we do not know the value of a, we cannot simplify this further.
|
