Function Concepts • Topic 2 of 5

Function Evaluation

To evaluate a function, substitute the given input value for every x in the rule and simplify. For f(x) = 3x − 4, f(5) = 3(5) − 4 = 11. Mind the order of operations: apply exponents before multiplying, and watch signs when the input is negative — f(−2) with f(x) = x² is (−2)² = 4, not −4. You can evaluate at numbers or at expressions. Careful substitution is the whole task, so use parentheses around the input to avoid sign and exponent mistakes. The SAT tests evaluation constantly, both on its own and as a step in larger problems.

A function machine: input 5 enters the rule f(x) = 3x minus 4 and outputs 11.Evaluating a function5inputf(x) = 3x − 411outputf(5) = 3(5) − 4 = 11

✅ Solved examples

1. If f(x) = 3x − 4, find f(5).
3(5) − 4 = 11.
2. If f(x) = x², find f(−3).
(−3)² = 9.
3. If f(x) = 2x + 7, find f(0).
2(0) + 7 = 7.
4. If f(x) = 4x − 1, find f(−2).
4(−2) − 1 = −9.

✏️ Practice — try these, take hints as needed

1. If f(x) = 5x − 3, find f(4).
Substitute x = 4.
5(4) − 3.
—
17.
2. If f(x) = x², find f(−5).
(−5)².
—
—
25.
3. If f(x) = 2x + 9, find f(0).
2(0) + 9.
—
—
9.
4. If f(x) = 3x − 6, find f(−1).
3(−1) − 6.
—
—
−9.
5. If f(x) = 6x + 2, find f(3).
6(3) + 2.
—
—
20.

📝 Topic test — 8 questions

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