Functions & Graphs 📊

Interactive Tutorial • Practice Problems • Speed Quiz

What is a Function? ⚙️

A **function** is a relationship where every input has exactly one output. Think of it like a machine: you put in a number (the **input** or $$x$$), the machine does some work, and a single number comes out (the **output** or $$y$$). We often write functions using **function notation**, like $$f(x)$$ which is read "f of x".

The **domain** is the set of all possible input values ($$x$$). The **range** is the set of all possible output values ($$y$$).

When we graph a function, we plot the pairs of inputs and outputs ($$x, y$$) on a coordinate plane. The graph is a visual representation of the function's behavior.

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Video: Graphing a Function from a Table 🎬

This video will walk you through how to create a graph from a function table step-by-step.

Practice Problems

Evaluate the function for the given value of x.

1) If $$f(x) = 3x + 2$$, find $$f(4)$$

$$f(4)$$ =

2) If $$f(x) = x^2 - 1$$, find $$f(3)$$

$$f(3)$$ =

3) If $$f(x) = 5 - x$$, find $$f(-2)$$

$$f(-2)$$ =

4) If $$f(x) = \frac{x}{2} + 3$$, find $$f(6)$$

$$f(6)$$ =

⚡ Functions Speed Quiz

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