Up to now, you are used to writing equations in the form "y =." For example, the following are typical linear equations:
| y = 4x + 5 y = -\(\mathsf{ \frac{1}{2} }\)x - 10 y = 2x - 6 |
Functions can also be written using function notation. Function notation exchanges the y = for f(x). We read function notation as "f of x."
| Click on each of the following equations to see them rewritten in function notation. | |
| y = 4x + 5 | f(x) = 4x + 5 |
| y = -\(\mathsf{ \frac{1}{2} }\)x - 10 | f(x) = -\(\mathsf{ \frac{1}{2} }\)x - 10 |
| y = 2x - 6 | f(x) = 2x - 6 |
Function notation is very useful when you are asked to evaluate a function for a certain value. For instance, let's say we have f(x) = -2x + 5 and want to find the value of f(x) when x is 2. We can simply write "f(2)" which means "f(x) when x = 2." In this example, f(2) would equal -2(2) + 5 = -4 + 5 = 1. So f(2) = 1. We would read this as "f of 2 equals 1".
Your Given Function Is...
f(x) = 4x + 30.
Find f(0) and f(-5).
Show all of your work.
| Let x equal zero. We write this as f(0). Substitute zero for the x value; then evaluate. f(x) = 4x + 30 f(0) = 4(0) + 30 f(0) = 0 + 30 f(0) = 30 |
Let x equal -5. We write this as f(-5). Substitute -5 for x in the equation; then evaluate. f(x) = 4x + 30 f(-5) = 4(-5) + 30 f(-5) = -20 + 30 f(-5) = 10 |
Your Given Function Is...
f(x) = -8x + 10.
Find f(0) and f(-5).
Show all of your work.
| Let x equal zero. We write this as f(0). Substitute zero for the x value; then evaluate. f(x) = -8x + 10 f(0) = -8(0) + 10 f(0) = 0 + 10 f(0) = 10 |
Let x equal -5. We write this as f(-5). Substitute -5 for x in the equation; then evaluate. f(x) = -8x + 10 f(-5) = -8(-5) + 10 f(0) = 40 + 10 f(0) = 50 |
