Math Snap

STEP 1

What is this asking?
We're given a piecewise function $f(x)$ and we need to find its value at $x = 2$, $x = 0$, and $x = 3$.
Watch out!
Piecewise functions can be tricky!
Make sure to plug in the $x$ value into the correct piece of the function.

STEP 2

1. Evaluate $f(2)$
2. Evaluate $f(0)$
3. Evaluate $f(3)$

STEP 3

Since $2 \neq 3$, we use the first piece of the function: $f(x) = \frac{x^2 - 9}{x - 3}$.
Let's plug in $x = 2$.
$$f(2) = \frac{2^2 - 9}{2 - 3}$$

STEP 4

Now, let's simplify the numerator and denominator:
$$f(2) = \frac{4 - 9}{2 - 3} = \frac{-5}{-1}$$

STEP 5

Dividing $-5$ by $-1$ gives us our result:
$$f(2) = 5$$

STEP 6

Since $0 \neq 3$, we again use the first piece: $f(x) = \frac{x^2 - 9}{x - 3}$. Substitute $x = 0$.
$$f(0) = \frac{0^2 - 9}{0 - 3}$$

STEP 7

Simplify the numerator and denominator:
$$f(0) = \frac{-9}{-3}$$

STEP 8

Dividing $-9$ by $-3$ gives us:
$$f(0) = 3$$

STEP 9

Now, $x = 3$, so we use the second piece of the function: $f(x) = 9$.
This one is super straightforward!
$$f(3) = 9$$

$f(2) = 5$
$f(0) = 3$
$f(3) = 9$