Hey there, young math whizzes! 🌟 Today, we're jumping into the fun world of functions. Think of functions as special machines that take an input, do something cool with it, and then give you an output. Let's find out how different numbers can change what comes out of a function!

What is a Function?

Basically, a function is a connection between a group of inputs (called the domain) and the possible outputs (called the range). Each input has one and only one output. This means if you put different numbers into the function, you'll get different results!

For example, here’s a simple function:

$f(x) = 2x + 3$

In this case, the function $f$ takes a number $x$, multiplies it by 2, and then adds 3.

Evaluating Functions: Let's Get Hands-On! 🎉

To see how different numbers change the output, we’re going to evaluate this function using a few inputs.

Step 1: Choose Your Values

Let’s pick some numbers for $x$:

• $x = 1$
• $x = 2$
• $x = 3$

Step 2: Plug Them In!

Now, let’s put these numbers into our function $f(x)$.

1. For $x = 1$:

   $$f(1) = 2(1) + 3 = 2 + 3 = 5$$

2. For $x = 2:$

   $$f(2) = 2(2) + 3 = 4 + 3 = 7$$

3. For $x = 3:$

   $$f(3) = 2(3) + 3 = 6 + 3 = 9$$

Step 3: Analyze the Output

Now, let’s take a look at our results:

• $f(1) = 5$
• $f(2) = 7$
• $f(3) = 9$

Wow! Check this out! When we increased the input $x$ from 1 to 3, the output $f(x)$ went up from 5 to 9. This shows us that the output of the function changes based on the value of $x$.

Conclusion: Values Matter!

To wrap it up, using different numbers in a function helps us see how the input directly changes the output. This is key to understanding how functions work! So, keep practicing, choose your values, and watch the cool outputs appear before your eyes. 🌈🎉 Happy calculating!