Math Snap

STEP 1

What is this asking?
We need to find which values of $x$ would cause trouble for the function $f(x)$, specifically making the denominator zero.
Watch out!
Don't mix up the numerator and denominator; we only care about the denominator here!
Also, be careful with the signs.

STEP 2

1. Examine the Denominator
2. Find the Restricted Value
3. State the Domain

STEP 3

Alright, so we've got this cool function, $f(x) = \frac{x - 3}{x + 5}$, and we're on the lookout for any domain restrictions.
What could possibly go wrong with this function?
Well, the only thing that could cause a problem is if we divide by zero.

STEP 4

Remember, dividing by zero is a big no-no in math!
It's like trying to divide a pizza into zero slices – it just doesn't make sense!
So, we need to make sure that the denominator of our function, $x + 5$, is never equal to zero.

STEP 5

Let's set up an equation to find the value of $x$ that would make the denominator zero:
$$x + 5 = 0$$

STEP 6

To solve for $x$, we need to get $x$ by itself.
We can do this by adding $-5$ to both sides of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!
$$x + 5 + (-5) = 0 + (-5)$$ $$x + 0 = -5$$$$x = -5$$

STEP 7

So, we found that when $x = -5$, the denominator becomes $-5 + 5 = 0$.
This is exactly what we're trying to avoid!

STEP 8

The domain of a function is all the possible values that $x$ can take.
Since we found that $x$ can be any value except $-5$, we can write the domain as $x \neq -5$.
This means $x$ can be any other number, big or small, positive or negative, but it just can't be $-5$.

The restriction on the domain of $f(x)$ is $x \neq -5$.