### Evaluate Functions With Graphs

What does * *ƒ(*x*) mean? Think of the function notation as a replacement for *y*. It reads "f of x."

- ƒ(
*x*) = 2*x*+ 1 is also known as*y*= 2*x*+ 1. - ƒ(
*x*) = |-*x*+ 5| is also known as*y*= |-*x*+ 5|. - ƒ(
*x*) = 5*x*^{2}+ 3*x*- 10 is also known as y = 5*x*^{2}+ 3*x*- 10.

### Other Versions of Function Notation

- ƒ(
*t*) = -2*t*^{2} - ƒ(
*b*) = 3*e*^{b} - ƒ(
*p*) = 10*p*+ 12

What do these variations of notation share? Whether the function begins with ƒ(*x*) or ƒ(*t*) or ƒ(*b*) or ƒ(*p*) or ƒ(♣), it means that the outcome of ƒ depends on what's in the parentheses.

- ƒ(
*x*) = 2*x*+ 1 (The value of ƒ(*x*) depends on the value of*x*.) - ƒ(
*b*) = 3*e*^{b}(The value of ƒ(*b*) depends on the value of*b*.)

Use this article to learn how to use a graph to find specific values of ƒ.

### Example 1: Linear Function

**What is ƒ(2)?**

In other words, when *x* = 2, what is ƒ(*x*)?

Trace the line with your finger until you get to the part of the line where *x* = 2. What is the value of ƒ(*x*)? 11

### Example 2: Absolute Value Function

**What is ƒ(-3)?**

In other words, when *x* = -3, what is ƒ(*x*)?

Trace the graph of the absolute value function with your finger until you're touching the point where *x* = -3. What is the value of ƒ(*x*)? 15

### Example 3: Quadratic Function

**What is ƒ(-6)?**

In other words, when *x* = -6, what is ƒ(*x*)?

Trace the parabola with your finger until you touch the point at which *x* = -6. What is the value of ƒ(*x*)? -18

### Example 4: Exponential Growth Function

**What is ƒ(1)?**

In other words, when *x *= 1, what is ƒ(*x*)?

Trace the exponential growth function with your finger until you touch the point at which *x* = 1. What is the value of ƒ(*x*)? 3

### Example 5: Sine Function

**What is ƒ(90°)?**

In other words, when x = 90°, what is ƒ(*x*)?

Trace the sine function with your finger until you touch the point at which *x* = 90°. What is the value of ƒ(*x*)? 1

### Example 6: Cosine Function

**What is ƒ(180°)?**

In other words, when x = 180°, what is ƒ(x)?

Trace the cosine function with your finger until you touch the point at which *x* = 180°. What is the value of ƒ(*x*)? -1