Functions — Drills
Functions has 7 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 3 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Slope — How much y changes for each 1 that x increases.
- y-intercept — The output when x = 0 — where the line crosses the vertical axis.
- Linear function — One whose graph is a straight line: y = mx + b.
Evaluating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If f(x) = 6x + 3, find f(9).
Worked answer
57
6(9) = 54
54 + 3 = 57
Problem 2
If f(x) = 8x + 0, find f(2).
Worked answer
16
8(2) = 16
16 + 0 = 16
Slope
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the slope of the line through (4, 1) and (10, 13).
Worked answer
2
13 - 110 - 4 = 126
= 2
Problem 2
Find the slope of the line through (3, 23) and (6, 38).
Worked answer
5
38 - 236 - 3 = 153
= 5
Intercepts
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A line has slope -4 and passes through (5, -18). Find its y-intercept.
Worked answer
2
-18 = -4(5) + b
-18 = -20 + b
b = 2
Problem 2
A line has slope 2 and passes through (1, 1). Find its y-intercept.
Worked answer
-1
1 = 2(1) + b
1 = 2 + b
b = -1
Rule
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A table gives x = 1, 2, 3 and y = 13, 21, 29. Write the rule in the form mx+b.
Worked answer
8x+5
Jump is 8, so the slope is 8
At x = 1: 8(1) + b = 13, so b = 5
y = 8x + 5
Problem 2
A table gives x = 1, 2, 3 and y = 5, 7, 9. Write the rule in the form mx+b.
Worked answer
2x+3
Jump is 2, so the slope is 2
At x = 1: 2(1) + b = 5, so b = 3
y = 2x + 3
Solvefn
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If f(x) = 8x + 4, find x when f(x) = 36.
Worked answer
4
8x = 32
x = 4
Problem 2
If f(x) = 2x + 1, find x when f(x) = 21.
Worked answer
10
2x = 20
x = 10
Linear
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which table shows a linear function?
- y = 8, 10, 12, 14
- y = 3, 4, 6, 9
- y = 1, 4, 9, 16
- y = 2, 4, 8, 16
Worked answer
y = 8, 10, 12, 14
y = 8, 10, 12, 14 jumps by 2 every time — linear.
The others square, double, or jump by changing amounts.
Word problems
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A gym charges $50 to join plus $22 a month. What does 6 months cost?
Worked answer
182
22 × 6 = 132
132 + 50 = 182
Problem 2
A gym charges $20 to join plus $18 a month. What does 18 months cost?
Worked answer
344
18 × 18 = 324
324 + 20 = 344