L10 · Function Notation for Linear Functions

Learning goal

“I can write a linear function in function notation, translate back to a two-variable equation, evaluate f at a numerical value, find the input that produces a given output, and describe the graph of a linear function given in function notation.”

Function notation — writing a function as f(x) (read "f of x") to name the function and show its input in one symbol.

f(x) — the OUTPUT of function f at input x; f(x) is a single quantity (it does NOT mean f times x). It plays the role of y.

Domain value — a chosen input; evaluating the function means computing the output for it.

Range value — an output; finding the domain value for it means solving an equation (e.g. find x so that f(x) = 15).

Worked example

Let f(x) = 3x - 2. The symbol f(4) is an instruction: "run the function f on the input 4." Everywhere x appears, put 4: f(4) = 3(4) - 2 = 10. So f(4) = 10, which is the ordered pair (4, 10) in disguise. Two more: f(0) = 3(0) - 2 = -2 (the y-intercept!), and f(-1) = 3(-1) - 2 = -5. Negative inputs are where sign errors live: 3(-1) is -3, then -3 - 2 = -5. And the translation both ways: y = 6x - 4 becomes f(x) = 6x - 4; f(x) = 3x + 9 becomes the equation y = 3x + 9. Only the name of the output changes.

Check yourself — explain it

f(4) = 10 means...

Paired problem — example still visible

For f(x) = 3x - 2, find f(2) and f(-3). -> f(2) = 4; f(-3) = 3(-3) - 2 = -11

Faded completion — last step is yours

"For g(x) = -x + 5: g(0) = ___; g(5) = ___; g(-2) = ___." -> 5; 0; 7

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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Grade 10 — Mathematics 10C › C10U07 Linear Relations & Functions

L10 · Function Notation for Linear Functions