Math 30-1 Chapter 1 Review Assignment p.1
Math 30-1 Chapter 1 Review
Function Transformations
Name ___________________________
Date reviewed with teacher:
Signature of teacher:
Math 30-1 Chapter 1 Review Assignment p.2
Math 30-1 Chapter 1 Review Assignment p.3
Math 30-1: Chapter 1 Review Assignment
Function Transformations
Answer the following questions. Remember to show all your work.
1. Given the graph of y  f  x  below, sketch the graph of y  2  f  x  3 .
y  f  x
y  2  f  x  3
2. Given y  k  a  x  h  , a  1 , h  0 , and k  0 , in which quadrant is the vertex?
2
(RF2)
(RF2)
Math 30-1 Chapter 1 Review Assignment p.4
3. Given the functions f  x   x  2  3 and g  x   x  2  1, describe the transformations the
will transform y  f  x  to become y  g  x  .
(RF2)
4. The transformation of the function f  x   x3 is described by the mapping notation
 x, y    x  2, y  5 .
Describe the transformations on y  f  x  .
(RF2)
5. The graph of f  x   x2 is below left. The function g  x  , sketched below right, is a
translation of f  x  . Determine the equation of g  x  .
f  x   x2
g  x   ______________________
(RF2)
Math 30-1 Chapter 1 Review Assignment p.5
6. Given the graph of y  f  x  below left, determine the equation of the graph below right
in the form y  k  f  x  h  .
y  f  x
(RF2)
New equation: ______________________
7. If you were given the graph of y  f  x  , describe the translations you would need to draw the
graph of y  k  f  x  h  , given that h  4 and k  2 .
(RF2)
Math 30-1 Chapter 1 Review Assignment p.6
8. The graph of y  f  x  is transformed into the graph of g  x   4  2 f  x  3 . The domain
and range of each functions is shown below. Complete the chart by filling in the domain and
range for the graph of g  x  .
(RF2)
Graph of f  x 
Domain
Range
 1,3
2,6
Graph of g  x 
9. The ordered pairs below represent possible transformations of the point P  a, b  on the graph
of the function y  f  x  .
Point 1:
 4a, b 
Point 3:
 a, b 
Point 2:
 a, b 
 b
Point 4:  a, 
 4
a 
Point 5:  , b 
4 
Point 6:
 a, 4b 
If y  f  x  undergoes the following single transformations, identify the coordinates of the
corresponding point P on the new graph.
a) The corresponding point on the function y   f  x  is point number _______.
(RF5)
1 
b) The corresponding point on the function y  f  x  is point number _______.
4 
(RF3)
1
f  x  is point number _______.
4
(RF3)
d) The corresponding point on the function y  f   x  is point number _______.
(RF5)
c) The corresponding point on the function y 
Math 30-1 Chapter 1 Review Assignment p.7
10. The graph of the function  f  x  is transformed to produce the graph of the function
y  g  x  as shown below. Determine an equation for g  x  in the form y  af  bx  .
11. Given the graph of y  f  x  below, sketch the graph of y 
y  f  x
1 1 
f  x .
2 3 
y
1 1 
f  x
2 3 
(RF3)
(RF3)
Math 30-1 Chapter 1 Review Assignment p.8
12. Given the graph of y  f  x  below, sketch the graph of y  2 f  3  x 1   1 .
y  f  x
(RF4)
y  2 f  3  x 1   1
13. The graph of y  f  x  is reflected in the x-axis, stretched vertically about the x-axis by a
1
, and stretch horizontally about the y-axis by a factor of 4 to create the graph of
3
y  g  x  . For the point  3, 6  on the graph of y  f  x  , determine the corresponding point
factor of
on the graph of y  g  x  .
(RF4)
Math 30-1 Chapter 1 Review Assignment p.9
14. If the point (-4, 7) is on the graph of y  f  x  , what point will be on the graph of
1

y  3 f   x  2    7 ?
4

(RF4)
15. Given the graph of y  f  x  below, determine the equation of the graph below right.
y  f  x
New equation: ______________________
(RF4)
Math 30-1 Chapter 1 Review Assignment p.10
16. Describe a sequence of transformations required to transform the graph of y  x to the graph
1
of y   x  4  10 .
2
(RF4)
17. Given the graph of y  ( x  3)2  6 below left, determine the equation of the graph below right.
(RF5)
y  ( x  3)2  6
New equation: ______________________
Math 30-1 Chapter 1 Review Assignment p.11
18. Given the graph of y  f  x  below, determine the equation of the graph below right.
y  f  x
(RF5)
New equation: ______________________
19. The graph of y   x 2  4 is reflected in the y-axis. Determine the equation of the new graph.
(RF5)
Math 30-1 Chapter 1 Review Assignment p.12
20. The graph of y  f  x  is shown below.
(RF5)
For each transformation of y  f  x  indicated, the invariant point exists at point number:
_______________
y   f  x
_______________
y  f  x
_______________
x  f  y
Math 30-1 Chapter 1 Review Assignment p.13
21. Given the graph of y  f  x  below, sketch the graph of y  f 1  x  .
y  f  x
(RF6)
y  f 1  x 
22. Explain a strategy for graphing x  f  y  , given the graph of y  f  x  .
(RF6)
Math 30-1 Chapter 1 Review Assignment p.14
23. Algebraically determine if the funtions y  2 x 2  7 and y  
1
x  7 are inverses of each
2
(RF6)
other.
24. a) Given that f  x    x  3  8 , determine the equation of y  f 1  x  .
2
(RF6)
b) What restrictions must be put on the domain of y  f  x  so that its inverse is a function?
(RF6)