What is f(x)? A Simple Explanation for Algebra 1 Students

📚 What is a Function?

In simple terms, a function is like a machine. You put something in (the input), and the machine gives you something else out (the output). The special thing about a function is that for every input, you always get the same output.

🧮 Understanding f(x) Notation

The notation "f(x)" is just a way to write a function. Here's what it means:

• 🏷️ "f" is the name of the function. You can call it anything, like "g" or "h", but "f" is common.
• 🔑 "x" is the input. It's the value you're putting into the function.
• 📦 "f(x)" is the output. It's the value you get after applying the function to "x". You can also think of $f(x)$ as 'y'.

➗ Example: A Simple Function

Let's say our function is $f(x) = 2x + 1$. This means: "Take the input (x), multiply it by 2, and then add 1."

• 🔢 If we put in $x = 3$, then $f(3) = 2(3) + 1 = 6 + 1 = 7$. So, the output is 7.
• ➕ If we put in $x = 0$, then $f(0) = 2(0) + 1 = 0 + 1 = 1$. So, the output is 1.
• ➖ If we put in $x = -1$, then $f(-1) = 2(-1) + 1 = -2 + 1 = -1$. So, the output is -1.

📊 Representing Functions

Functions can be represented in a few ways:

• 🖋️ Equation: Like $f(x) = 2x + 1$ (the example above).
• 📈 Graph: A visual representation on a coordinate plane.
• 💼 Table: A table showing inputs (x) and their corresponding outputs (f(x)).

Here's an example of a table for $f(x) = 2x + 1$:

✍️ Practice Quiz

Let's test your understanding. For the function $f(x) = x - 5$, find the following:

• ❓ What is $f(10)$?
• ❓ What is $f(0)$?
• ❓ What is $f(-5)$?
• ❓ What is $f(5)$?
• ❓ What is $f(2)$?
• ❓ What is $f(-1)$?
• ❓ What is $f(1)$?

Answers:

1. $f(10) = 5$
2. $f(0) = -5$
3. $f(-5) = -10$
4. $f(5) = 0$
5. $f(2) = -3$
6. $f(-1) = -6$
7. $f(1) = -4$