1. Let's start by defining a simple function to understand how it works. 2. A function is a rule that assigns each input exactly one output. 3. For example, consider the function $$f(x) = 2x + 3$$. 4. This means for any input value $x$, the output is calculated by multiplying $x$ by 2 and then adding 3. 5. Let's calculate some values: - If $x = 1$, then $$f(1) = 2 \times 1 + 3 = 2 + 3 = 5$$. - If $x = 2$, then $$f(2) = 2 \times 2 + 3 = 4 + 3 = 7$$. - If $x = -1$, then $$f(-1) = 2 \times (-1) + 3 = -2 + 3 = 1$$. 6. This shows how the function takes an input and produces an output. 7. The general form of a linear function is $$f(x) = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 8. In our example, $m=2$ and $b=3$. 9. This function can be graphed as a straight line with slope 2 and y-intercept 3. 10. Understanding this helps you see how functions map inputs to outputs clearly.