Writing & Transforming Linear Functions — Drills
Writing & Transforming Linear Functions has 5 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 10 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Arithmetic sequence — A list that grows by adding the same amount each time.
- Function — A rule pairing each input with exactly one output.
- Slope — How much y changes for each 1 that x increases.
- Linear function — One whose graph is a straight line: y = mx + b.
- Rate of change — The slope, in the units of the situation.
- Average rate of change — f(b) - f(a)b - a over an interval.
- Transformation — A change to the function that moves or stretches its graph.
- Sequence — An ordered list of numbers. The nth one is an.
- Explicit formula — A rule giving an directly from n.
- Common difference — The constant added each time, in an arithmetic sequence.
Model
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A service charges $53 up front plus $35 an hour. Write C(h).
Worked answer
C(h) = 35h + 53
b = 53
m = 35
C(h) = 35h + 53
Problem 2
A service charges $72 up front plus $28 a day. Write C(d).
Worked answer
C(d) = 28d + 72
b = 72
m = 28
C(d) = 28d + 72
Rate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x) = 7x + 5, what is the rate of change?
Worked answer
7
m = 7
Constant everywhere, because the function is linear.
Problem 2
For f(x) = -7x + 1, what is the rate of change?
Worked answer
-7
m = -7
Constant everywhere, because the function is linear.
Arith
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the 28th term of 7, 10, 13, ….
Worked answer
88
7 + 27(3)
= 7 + 81
= 88
Problem 2
Write an explicit formula for 14, 18, 22, 26, ….
Worked answer
a_n = 14 + 4(n - 1)
a1 = 14, d = 4
an = 14 + (n-1)(4)
Or 4n + 10
Avgrate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x) = 4x2 + 1, find the average rate of change from x = 1 to x = 7.
Worked answer
32
f(1) = 5
f(7) = 197
197 - (5)7 - 1 = 32
Problem 2
For f(x) = 1x2 - 1, find the average rate of change from x = 3 to x = 8.
Worked answer
11
f(3) = 8
f(8) = 63
63 - (8)8 - 3 = 11
Shift
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
The graph of f(x) is shifted 5 units left. Write the new function.
Worked answer
f(x + 5)
Add 5 inside the brackets — inside is reversed.
f(x + 5)
Problem 2
The graph of f(x) is shifted 7 units left. Write the new function.
Worked answer
f(x + 7)
Add 7 inside the brackets — inside is reversed.
f(x + 7)