Function Notation
Functions are usually written using function notation like f(x), read “f of x,” where f names the rule and x is the input variable.
This is a free explanation of Function Notation — a preview, not the full interactive lesson. The lesson, practice, quizzes, and AI Tutor are inside the app.
The most common form is f(x). Here f is the name of the function and x is the input variable. You will also see g(x), h(x), and other letters — the letter is just a label, like a name tag on the rule.
Important: f(x) does NOT mean “f multiplied by x.” It means “apply rule f to input x.” When you see f(3), replace every x in the formula with 3 and simplify. When you see f(−2), replace every x with −2 — a negative input always goes in parentheses before you apply any exponents or multiply.
To evaluate a function is to find the output for a specific input: write the function, substitute the given value for every x, then simplify using order of operations. Pay close attention to signs.
Worked example
Evaluate g(x) = −2x + 5 at x = −3.
- Write the function: g(x) = −2x + 5.
- Substitute x = −3, keeping the negative in parentheses: g(−3) = −2(−3) + 5.
- Multiply first: −2 × −3 = +6. Two negatives multiply to a positive.
- Then add: 6 + 5 = 11.
g(−3) = 11
On the test: The GED & HiSET also test reverse evaluation — given the output, find the input by setting f(x) equal to it and solving.
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