Function Concepts • Topic 1 of 5

Function Notation

Function notation writes a rule as f(x), read “f of x,” where x is the input and f(x) is the output. The letter f is just a name; g(x) and h(x) work the same way. Writing f(3) means “evaluate the function at x = 3.” The notation does not mean f times x — it names an output. A statement like f(2) = 7 says the input 2 produces the output 7. Understanding this lets you read graphs and tables of functions and translate between “the value of the function at 2” and f(2). The SAT relies on fluent reading of this notation throughout the Advanced Math section.

A function machine: input 3 enters the rule f(x) = 2x squared + 1 and outputs 19.Function notation3inputf(x) = 2x² + 119outputf(3) = 2(3)² + 1 = 19

✅ Solved examples

1. If f(x) = 2x² + 1, find f(3).
2(3²) + 1 = 18 + 1 = 19.
2. What does f(2) = 7 tell you?
The input 2 gives the output 7.
3. If g(x) = 5x, find g(4).
5 × 4 = 20.
4. If f(x) = 3x² + 2, find f(2).
3(4) + 2 = 14.

✏️ Practice — try these, take hints as needed

1. If f(x) = 4x² + 1, find f(2).
Substitute x = 2.
4(4) + 1.
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17.
2. If f(x) = 2x² + 3, find f(3).
2(9) + 3.
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21.
3. What does f(5) = 12 mean?
Input → output.
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The input 5 gives the output 12.
4. If h(x) = 6x, find h(7).
6 × 7.
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42.
5. If f(x) = 5x² + 2, find f(2).
5(4) + 2.
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22.

📝 Topic test — 8 questions

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