💡 What You Will Learn
Function evaluation means plugging a number into a function and calculating the result. When you see f(3), it means "replace every x with 3 in the function, then simplify." This topic appears on every GED Math exam — and once you learn the 4-step method, it becomes straightforward!
f(x) is read as "f of x" — it means the function named f, applied to the input x.
f(3) means: take the function f and replace every x with 3.
g(−1) means: take the function g and replace every x with −1.
The name could be f, g, h, or any letter. They all work the same way — plug in the value and calculate.
Every time you see x in the formula, you swap it with the given number. If x = 3, replace every x with 3.
If x = −2, write (−2) — not just −2. This is critical for squaring: (−2)² = 4, not −4!
If f(x) = 3x + 1, what does f(4) mean? (Replace x with 4: 3·4 + 1 = ?)
Read the problem carefully. Find the function formula and the value you need to substitute.
Example: "Find f(2) for f(x) = 2x² + 3x − 4" → function: 2x² + 3x − 4, value: x = 2
Write out the full expression with the number substituted in.
f(2) = 2(2)² + 3(2) − 4
Use parentheses, especially for negative values!
Exponents first → then multiply/divide → then add/subtract.
(2)² = 4 → 2·4 = 8 → 3·2 = 6
8 + 6 − 4 = 10
The result is the value of the function for that input. ✅
| Step | Action | Example |
|---|---|---|
| 1 — Identify | Find the function & value | f(x)=2x²+3x−4, x=2 |
| 2 — Substitute | Replace every x with ( value ) | 2(2)²+3(2)−4 |
| 3 — Operate | Powers → × ÷ → + − | 8 + 6 − 4 |
| 4 — Simplify | Final answer | = 10 ✅ |
Using the same function f(x) = 2x² + 3x − 4, what is f(3)? (Substitute 3 for every x)
When substituting a negative value, always write it in parentheses: (−1) not just −1.
This prevents sign errors: (−1)² = +1 but −1² = −1. Big difference on the GED!
Using the same function g(x) = x² − 4x + 7, what is g(−2)? (Remember: use parentheses for (−2)!)
Using the same function h(x) = (1/2)x² − 3x + 8, what is h(2)? (Step 1: (2)²=4, Step 2: (1/2)×4=2...)
Try f(x)=2x²+3x−4 with x=2 → should get 10 | Try g(x)=x²−4x+7 with x=−1 → should get 12 | Try h(x)=(1/2)x²−3x+8 with x=4 → should get 4