Parent Functions & Transformations — Drills
Parent Functions & Transformations 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 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Absolute value — |x| — distance from zero, always positive or zero.
- Open — Open excludes the endpoint (<, >); closed includes it (≤, ≥).
- Vertex — A flat surface; a line where two faces meet; a corner point.
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Factor — A number that divides evenly into another.
- Function — A rule pairing each input with exactly one output.
- Parabola — The U-shaped graph of a quadratic function.
- Height — The perpendicular distance from the base to the opposite corner.
Vertex
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the vertex of y=(x+2)2-6.
Worked answer
(-2,-6)
x+2=0 at x=-2
The constant outside gives y=-6
Problem 2
Give the vertex of y=(x-4)2+1.
Worked answer
(4,1)
x-4=0 at x=4
The constant outside gives y=1
Shift
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
The graph of y=(x+5)2 is the graph of y=x2 moved which way, and by how much? Give the number of units.
Worked answer
5
x+5=0 at x=-5
So the graph has moved left by 5
Problem 2
The graph of y=(x+7)2 is the graph of y=x2 moved which way, and by how much? Give the number of units.
Worked answer
7
x+7=0 at x=-7
So the graph has moved left by 7
Start
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
At what x does the graph of y=√x+6 begin?
Worked answer
-6
x+6 ≥ 0
x ≥ -6
Problem 2
At what x does the graph of y=√x+8 begin?
Worked answer
-8
x+8 ≥ 0
x ≥ -8
Writing the expression
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
An absolute value graph has its corner at (-4, 8) and is not stretched. Write its equation.
Worked answer
y=|x+4|+8
Corner at x=-4 gives |x+4|
Corner at y=8 gives +8 outside
Problem 2
An absolute value graph has its corner at (-5, -4) and is not stretched. Write its equation.
Worked answer
y=|x+5|-4
Corner at x=-5 gives |x+5|
Corner at y=-4 gives -4 outside
Piece
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x)=x+5 when x<3, and f(x)=x2 when x ≥ 3, find f(2)+f(3).
Worked answer
16
2<3, so f(2)=2+5=7
3 ≥ 3, so f(3)=9
Sum =16
Problem 2
For f(x)=x+4 when x<4, and f(x)=x2 when x ≥ 4, find f(-1)+f(8).
Worked answer
67
-1<4, so f(-1)=-1+4=3
8 ≥ 4, so f(8)=64
Sum =67
Stretch
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
How many times taller is y=6|x| than y=|x|?
Worked answer
6
Every height is multiplied by 6
Problem 2
How many times taller is y=2|x| than y=|x|?
Worked answer
2
Every height is multiplied by 2