Grade 8 Mathematics
A FUNCTION is a special relationship where each INPUT has exactly ONE OUTPUT.
Think of it like a machine: Put a number in, get ONE number out. Same input = same output every time!
f(x) is read as "f of x" - it means "the output when x is the input"
Example: If f(x) = 2x + 3, then:
f(4) = 2(4) + 3 = 8 + 3 = 11 (input is 4, output is 11)
Check: Does any x-value repeat with different y-values?
YES - Function!
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 5 | 7 | 9 | 11 |
Each x has one y
NO - Not a Function!
| x | 1 | 2 | 1 | 3 |
|---|---|---|---|---|
| y | 5 | 7 | 8 | 9 |
x = 1 gives 5 AND 8!
If ANY vertical line crosses the graph MORE than once, it's NOT a function!
Function
Line hits once
Not a Function
Line hits twice!
Given f(x) = 3x - 5, find f(4)
Identify the input: We need to find f(4), so the input is 4
Replace x with 4: f(4) = 3(4) - 5
Calculate: f(4) = 12 - 5 = 7
LINEAR: Straight line graph
Equation: y = mx + b (no exponents on x)
Example: f(x) = 2x + 1
NON-LINEAR: Curved graph
Equation has x², x³, or curves
Example: f(x) = x² + 1
1. Is this a function?
| x | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| y | 3 | 5 | 7 | 9 |
Answer: YES / NO (circle one) Explain: _______________________
2. If f(x) = 4x + 2, find:
a) f(3) =
b) f(0) =
c) f(-2) =
3. Is this relation a function? {(1, 4), (2, 5), (3, 6), (2, 7)}
Answer: YES / NO Why? _______________________________________
4. Which is LINEAR and which is NON-LINEAR?
a) f(x) = x² - 4 → ________________
b) f(x) = 5x - 3 → ________________
c) f(x) = 2/x → ________________