Functions
GradesGrade 8FunctionsWhat Is a Function?

What Is a Function?

🔗 Functions
⚙️

What Is a Function?

A function assigns each input exactly one output — like a reliable machine.

A function is a rule that assigns each input (from the domain) to exactly one output (in the range). If any input maps to two or more outputs, the relationship is NOT a function. Think of a function as a machine: one ingredient in, one product out.

f:x↦f(x)(one input x gives exactly one output f(x))f: x \mapsto f(x) \quad \text{(one input } x \text{ gives exactly one output } f(x))

Function ✓

Input 1 → Output 5Input 2 → Output 7Input 3 → Output 5 (OK — different inputs can share outputs)Each input has exactly ONE output

Not a Function ✗

Input 2 → Output 5Input 2 → Output 9 (FAILS — same input, two outputs!)One input has TWO outputs

Vertical Line Test: if any vertical line crosses a graph more than once, it is NOT a function.

📋Checking a table for functions
x:  1   2   3   2
f:  4   7   9   3  ← x = 2 maps to both 7 and 3. NOT a function!

x:  1   2   3   4
f:  4   7   9   12  ← each x has one f(x). This IS a function.
💡

Remember This!

In a set of ordered pairs, check if any x-value repeats with a different y-value. One repeat with the SAME y-value is still a function; a repeat with a DIFFERENT y-value is not.

✏️ Try It!

Which set of ordered pairs represents a function?

Practice with CalcVerse
📈Line Grapher (y = mx + b)
Take Quiz 📝 — 26 Questions