Pure Math 30
Transformations Review
1. Describe how the graph of y = f(x) + 2 can be obtained from the graph
of y = f(x).
2. Describe how the graph of y = 0.5f(2x) can be obtained from the
graph of y = f(x).
3. The graph of y = f(x) is shown. Sketch the graph of y = 2f(x + 3).
4. Given f(x) = 2(x + 1)2 – 3
a) write the equation for y = -f(x)
b) graph y = f(x) and y = -f(x) and describe how they are related
c) describe how y = f(x) and y = f(-x) compare
7
5. Given the function f ( x)  2
x 1
a) sketch the graph of the function
b) write an equation for the inverse function
6. How do the graphs of y = (2x)3 and y = 2x3 compare to y = x3?
7. The graph of f(x) = x is stretched horizontally about the y-axis by a
factor of one third, reflected in the y-axis and translated 4 units up.
Write the equation of the transformed function.
8. Given f(x) = x(x + 2)(x – 3)
a) determine the zeros of y = f(2x)
b) determine the zeros of y = 3f(-x)
9. Describe in words how the graph of y 
1
 1 could be obtained
x3
1
.
x
10. Given y = (x – 1)2, write the equation for y = -f(x), y = f(-x) and x =
f(y).
from the graph of y 
Answers: 1. vertical translation up 2 2. stretched vertically about the x-axis factor of 0.5 and horizontally about
the y-axis factor of 0.5 4.a) y = -2(x+1)2+3 b)reflected in x-axis c)reflected in y-axis 5.b)x=7/(y2+1) or y=(7/x-1)
6.stretched horizontally about the y-axis factor of 0.5; stretched vertically about x-axis factor of 2 7. y=(-3x)+4
8.a)0,-1,1.5 b)0,2,-3 9.horizontal translation 3 right and vertical translation 1 up 10. y=-(x-1)2, y=(-x-1)2, y=1x