Mastering SAT Functions
The Core Concept
On the SAT, functions are simply rules that map an input to exactly one output. Think of the
notation f(x) as a replacement for y on the coordinate plane.
Input (x) → Function [f(x)] → Output (y)
Key Function Skills
- Substitution: If given f(x), find f(3) by replacing every x in the equation with 3.
- Nested Functions: For g(f(x)), solve the inner function first, then use that result as the input for the outer function.
- Graphs: Understand that the solution to f(x) = k is the x value where the graph hits the height of k.
Example Problem
If f(x) = 3x ² − 5 and g(x) = 2x + 1, what is the value of f(g(2))?
Setup:
Step 1: Find g(2) = 2(2) + 1 = 5
Step 2: Find f(5) = 3(5)² − 5
Step 3: f(5) = 3(25) − 5 = 75 − 5
Step 4: f(5) = 70
Result: 70
Pro Tip: When the SAT asks for "zeros" or "roots" of a function, they are simply asking for the x-intercepts where f(x) = 0.