SAT Math: Function Notation
40+ practice questions in Praczo
The concept, explained
- 1
f(x) means "the output of function f when the input is x." It is not multiplication — f(3) means evaluate f at x = 3.
- 2
To find f(a), substitute a for every x in the function definition. If f(x) = 2x² − 1, then f(3) = 2(9) − 1 = 17.
- 3
f(x + 1) means substitute the entire expression (x + 1) for x: if f(x) = 3x, then f(x + 1) = 3(x + 1) = 3x + 3.
- 4
When the SAT says "f(k) = 5," set the function equal to 5 and solve for k.
- 5
On a graph, f(a) is the y-value at x = a. If the graph passes through (3, 7), then f(3) = 7.
- ✗ Treating f(2) as "f times 2." f(2) means plug in 2 — it has nothing to do with multiplication.
- ✗ Assuming f(x + 2) = f(x) + 2. This only holds for linear functions. For quadratics and others, always substitute fully.
SAT-style practice
If f(x) = x² − 3x + 4, what is the value of f(−2)?
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