What Is a Function? — Drills
What Is a Function? has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
- Function — A rule pairing each input with exactly one output.
- Slope — How much y changes for each 1 that x increases.
- Domain — The set of allowed inputs.
- Range — The set of outputs that actually occur.
- Parabola — The U-shaped graph of a quadratic function.
Isfunction
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Is {(3, 4), (5, 1), (7, 2)} a function? Answer yes or no.
Worked answer
yes
Inputs are 3, 5, 7 — all different.
Each has exactly one output, so yes.
Problem 2
Is {(3, 7), (7, 8), (3, 8)} a function? Answer yes or no.
Worked answer
no
The input 3 appears twice.
It goes to 7 and to 8.
So it is not a function.
Evaluating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If f(x) = 3x2 + 1, find f(6).
Worked answer
109
(6)2 = 36
3(36) = 108
108 + 1 = 109
Problem 2
If f(x) = 4x2 - 2, find f(0).
Worked answer
-2
(0)2 = 0
4(0) = 0
0 - 2 = -2
Vertical
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which graph fails the vertical line test?
- A straight line with slope 3
- A sideways parabola
- A horizontal line
- A parabola opening upward
Worked answer
A sideways parabola
Slide a vertical line across each graph.
A sideways parabola is crossed twice, so one x has two y values.
That is not a function.
Linear
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Is this table linear? x: 1, 2, 3, 4; y: 5, 10, 15, 20. Answer yes or no.
Worked answer
yes
Differences: 5, 5, 5
Constant, so linear with slope 5.
Problem 2
Is this table linear? x: 1, 2, 3, 4; y: 3, 5, 7, 9. Answer yes or no.
Worked answer
yes
Differences: 2, 2, 2
Constant, so linear with slope 2.
Domain
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x) = 1x + 6, which value must be excluded from the domain?
Worked answer
-6
The denominator is zero when x = -6.
So exclude x = -6.
Problem 2
For f(x) = 1x + 1, which value must be excluded from the domain?
Worked answer
-1
The denominator is zero when x = -1.
So exclude x = -1.
Range
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x) = x2 with domain {-3, -2, -1, 0, 1, 2, 3}, list the range.
Worked answer
{0, 1, 4, 9}
Squares: 9, 4, 1, 0, 1, 4, 9
Distinct values: 0, 1, 4, 9
Problem 2
For f(x) = x2 with domain {-2, -1, 0, 1, 2}, list the range.
Worked answer
{0, 1, 4}
Squares: 4, 1, 0, 1, 4
Distinct values: 0, 1, 4