When we jump into functions in Grade 9 Pre-Calculus, one cool thing we get to learn about is dividing functions! Ready to learn? Let's make it easy to understand!

What is Function Division?

Dividing functions means taking two functions and creating a new one by dividing one by the other.

If we have two functions, $f(x)$ and $g(x)$, we can show the division like this:

$$\frac{f(x)}{g(x)} \quad \text{(but remember, } g(x) \text{ can’t be zero!)}$$

This means we can only use the new function where $g(x)$ is not equal to zero. That’s because you can't divide by zero!

Steps to Divide Functions

Here’s how to divide functions in a few simple steps:

1. Identify the Functions: Find out which two functions you’re using: $f(x)$ (the top part) and $g(x)$ (the bottom part).

2. Set It Up: Write it like this: $h(x) = \frac{f(x)}{g(x)}$.

3. Simplify: If you can, make it easier! Look for common factors in $f(x)$ and $g(x)$ that you can cancel out.

Example Time!

Let’s say we have:

• $f(x) = x^2 - 1$
• $g(x) = x - 1$

To divide these functions, we set it up like this:

$$h(x) = \frac{x^2 - 1}{x - 1}$$

Next, we can factor $f(x)$:

$$h(x) = \frac{(x - 1)(x + 1)}{x - 1}$$

Now, we can cancel out the $(x - 1)$ terms (but remember, $x$ can’t be 1):

$$h(x) = x + 1 \quad \text{(as long as } x \neq 1\text{)}$$

Wrap-Up

Dividing functions isn’t just about making math easier; it helps you see how functions work together! So grab your math supplies and keep exploring! The more you divide, the more fun you’ll have! 🎉