Use function notation f(x) and describe relationships. Math 10-C Alberta mathematics.
Lesson 7.4 of Relations and Functions in Math 10C — Alberta curriculum lessons.
What f(x) = ... Really Says. Function notation is a compact way to write a function.
Instead of writing y = , we write f(x) = .
The letter f is the name of the function — you will also see g(x), p(x), h(m), and so on.
The part in brackets — (x) — is the input (the independent variable).
The expression on the right describes how the output is calculated from that input.
Wedding Catering Example — f(x) = 15x + 100. A caterer charges \15 per person, plus a flat \100 fee.
In plain English: "The cost, f(x), equals \15 times the number of people (x), plus a fixed \100."
The 15x part is the rate — it grows with the number of people.
The +100 part is the flat starting amount — it is always charged, regardless of the guest count.
The Letter Does Not Matter. "f(x)" means "a function of x." What matters is the part in brackets — that is the input.
You will see g(x), p(x), h(m), and other names. They all work the same way.
Example — Cost for 20 People. Find the cost for 20 people using f(x) = 15x + 100.
Step 1 — Replace x with 20:
f(20) = 15(20) + 100
Step 2 — Multiply:
f(20) = 300 + 100
Step 3 — Add:
Answer: f(20) = 400, so 20 people cost \400.
Critical Tip — f(20) Does NOT Mean f × 20. f(20) means "the value of the function when the input is 20." It is never a multiplication.
Always substitute the number for x — never multiply the function name by the number.
Example 1 — Taxi: \3 flat pickup + \2 per km. Identify the parts:
Rate: \2 per km → 2x
Flat amount: \3 pickup fee → +3
Answer: f(x) = 2x + 3, where x = kilometres driven.
Example 2 — Minimum Wage: \15/hour, no flat fee. Identify the parts:
Rate: \15 per hour → 15x
Flat amount: none → no constant term
Answer: f(x) = 15x, where x = hours worked.
Example 3 — Serving Job: \15/hour + \30 tips daily. Identify the parts:
Rate: \15 per hour → 15x
Flat amount: \30 daily tips → +30
Answer: f(x) = 15x + 30, where x = hours worked.
Example 4 — Cell Phone: \5.00 monthly + \0.05 per text. Identify the parts:
Rate: \0.05 per text → 0.05x
Flat amount: \5.00 monthly fee → +5
Answer: f(x) = 0.05x + 5, where x = number of texts.
Example 5 — Car Rental: \40 flat + 2 cents per km. Identify the parts:
Rate: 2 cents = \0.02 per km → 0.02x
Flat amount: \40 rental fee → +40
Answer: f(x) = 0.02x + 40, where x = kilometres driven.
Watch out: 2 cents must be written as \0.02, not 2. Mixing cents and dollars is the most common error.
Example 6 — Water (Lacombe): \73.75 hookup + \3.91 per cubic metre. Build the function:
f(x) = 3.91x + 73.75, where x = cubic metres used.
Evaluate for 10 cubic metres:
f(10) = 3.91(10) + 73.75
f(10) = 39.10 + 73.75
Answer: f(10) = 112.85, so 10 cubic metres costs \112.85.
Example 7 — Celsius to Fahrenheit: (9)/(5) times Celsius + 32. Build the function:
f(x) = (9)/(5)x + 32, where x = temperature in Celsius and f(x) = Fahrenheit.
Verify with 0°C:
f(0) = (9)/(5)(0) + 32 = 32°F ✓
Verify with 100°C:
f(100) = (9)/(5)(100) + 32 = 180 + 32 = 212°F ✓
Key point: the (9)/(5) multiplies the Celsius temperature, and 32 is added at the end.
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