Function — Grade 7 Math, what it means and where it is taught
A rule pairing each input with exactly one output.
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Transformation — A change to the function that moves or stretches its graph.
- Parabola — The U-shaped graph of a quadratic function.
- Piecewise function — A function defined by different rules on different intervals.
- Composition — Running one function on the output of another, written (f ° g)(x) = f(g(x)).
- Inverse function — The function that undoes another, written f-1. It sends every output back to the input it came from.
- One-to-one — No two inputs share an output. Only a one-to-one function has an inverse that is itself a function.
- Horizontal line test — If any horizontal line meets a graph twice, the function is not one-to-one.
- Domain of a composition — The inputs that survive both machines — the inner function must produce something the outer one accepts.
- Restricted domain — The stretch of the original function kept so that it is one-to-one.
- Limit — The value a function approaches as the input approaches some number.
- Continuous — A function you could draw without lifting the pen — no holes, jumps or blow-ups.
Practise this idea
18 questions in the course bank use Function, in What Is a Function?, Writing & Transforming Linear Functions, Exponential Functions & Growth, Composing & Inverting Functions, Parent Functions & Transformations, Inverse Trigonometric Functions. The first 8 are below; the rest are in those units.
Problem 1
Is {(1, 3), (2, 5), (3, 7)} a function?
- Yes
- No, because the outputs differ
- No, because 1 is an input
- Not enough information
Worked answer
Yes
Inputs are 1, 2, 3 — all different
Each has exactly one output
So yes
Problem 2
Is {(4, 1), (5, 2), (4, 9)} a function?
- No, because the input 4 has two outputs
- Yes
- No, because 9 is too large
- Yes, because all outputs differ
Worked answer
No, because the input 4 has two outputs
4 appears twice, with 1 and with 9
One input must have exactly one output
So it is not a function
Problem 3
Which graph fails the vertical line test?
- A circle
- A straight line with slope 2
- A parabola opening up
- A horizontal line
Worked answer
A circle
A circle is crossed twice by most vertical lines
So one x gives two y values
It is not a function
Problem 4
Which set is a function?
- {(1, 5), (2, 5), (3, 5)}
- {(5, 1), (5, 2), (5, 3)}
- {(1, 2), (1, 3)}
- {(0, 0), (0, 1)}
Worked answer
{(1, 5), (2, 5), (3, 5)}
The first has inputs 1, 2, 3 — all different
The others all repeat an input
Problem 5
A function has f(2) = 7 and f(6) = 19 and is linear. Find f(10).
Worked answer
31
m = 19 - 76 - 2 = 3
From f(6) = 19, four more steps of 3
19 + 12 = 31
Problem 6
The graph of f(x) is shifted 4 units up. Write the new function.
Worked answer
f(x) + 4
f(x) + 4
Problem 7
The graph of f(x) is shifted 3 units right. Write the new function.
Worked answer
f(x - 3)
f(x - 3)
This is the one that feels backwards
Problem 8
A function has f(3) = 12 and f(11) = -4. Find the average rate of change.
Worked answer
-2
-4 - 1211 - 3
= -168 = -2