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.
Create a free Studyio account to take the full lesson with voice-over teaching, practice questions and instant feedback.