L1 · One situation, four representations: words, table, graph, equation

Learning goal

“I can take one real-world situation and move between its four representations - a description in words, a table, a described graph, and an equation in function notation - and I can evaluate f(a) and find the input when I am given the output.”

Function — a relationship where each input has exactly ONE output.

Function notation — writing a function as f(x) = (rule), e.g. f(x) = 2x + 3. The letter names the function; the value in parentheses is the input.

Input — the value fed INTO the function (the x). It is chosen freely (within the domain, L3).

Output — the value the function RETURNS (the f(x)). f(3) is read "f of 3" and means the output when the input is 3 - it is NOT f times 3.

Worked example

A plumber charges a $60 call-out fee plus $45 per hour of work. Let C(h) be the total cost, in dollars, of a job lasting h hours. Words: "start at 60, then add 45 for every hour." Table: h = 0, 1, 2, 3, 4 -> C(h) = 60, 105, 150, 195, 240. Equation: C(h) = 45h + 60. The 60 is the value at h = 0 (the fee, paid before any work happens); the 45 is what each additional hour adds - the slope, wearing its units: $45 per hour. Evaluating: C(3) = 45 x 3 + 60 = 135 + 60 = 195 - "a 3-hour job costs $195." Say the reading out loud: the INPUT goes inside the parentheses; the OUTPUT is the whole value f(input). C(3) = 195 is one complete sentence: input 3, output 195.

Check yourself — explain it

In C(h) = 45h + 60, the number 60 represents...

Paired problem — example still visible

An electrician charges a $50 call-out fee plus $40 per hour. Write E(h) and find E(2). -> E(h) = 40h + 50; E(2) = 80 + 50 = 130 (a 2-hour job costs $130).

Faded completion — last step is yours

"A gym charges a $30 sign-up fee plus $12 per month. M(m) = ___ m + ___. M(6) = ___" -> 12; 30; 102

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

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