Skill: Evaluate functions using function notation

Function notation tells you which input to use. In $f(a)$, the number or expression inside the parentheses is the input, and $f(a)$ is the corresponding output. It does not mean $f \times a$.

To evaluate a function:

1. Identify the input inside the parentheses.
2. Substitute that input everywhere the variable appears.
3. Use parentheses, especially for negative numbers.
4. Simplify using the order of operations.

Suppose

$$f(x)=2x^2-3x+1$$

Find $f(-2)$.

The input is $-2$, so replace every $x$ with $(-2)$:

$$f(-2)=2(-2)^2-3(-2)+1$$

Now simplify the exponent and multiplication:

$$f(-2)=2(4)+6+1$$

Finally, add:

$$f(-2)=8+6+1=15$$

Therefore,

$$\boxed{f(-2)=15}$$

This means that the function’s output is $15$ when the input is $-2$. On a graph, this corresponds to the point $(-2,15)$.