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Study Guide for Parent Functions, Transformations, and Systems of Equations
The graph of a function is given. Name the parent function. Then state the domain, range, zeros, and intervals
where the function is increasing and/or decreasing.
1) 2)
3) 4)
Parent function:________________Zeros:_________
Domain:_______________ Range:______________
Decreasing: _____________ Increasing:____________
Parent function:________________Zeros:_________
Domain:_______________ Range:______________
Decreasing: _____________ Increasing:____________
Parent function:________________Zeros:_________
Domain:_______________ Range:______________
Decreasing: _____________ Increasing:____________
Parent function:________________Zeros:_________
Domain:_______________ Range:______________
Decreasing: _____________ Increasing:____________
5) 6)
7) 8)
Parent function:________________Zeros:_________
Domain:_______________ Range:______________
Decreasing: _____________ Increasing:____________
Parent function:________________Zeros:_________
Domain:_______________ Range:______________
Decreasing: _____________ Increasing:____________
Parent function:________________Zeros:_________
Domain:_______________ Range:______________
Decreasing: _____________ Increasing:____________
Parent function:________________Zeros:_________
Domain:_______________ Range:______________
Decreasing: _____________ Increasing:____________
Describe the transformations to the parent functions given below.
9) ( ) ( ) 10) ( ) ( )
11) ( )
12) ( )
13) ( ) ( ) 14) ( ) ( )
15) ( )
( ) 16) ( ) |
|
17) ( ) √ 18) ( ) √
19) ( ) | | 20) ( ) √
21) ( ) (
)
22) ( )
23) ( ) ( ) 24) ( ) ( )
25) Given the parent function ( ) | | write the function rule if the following transformations are done on
the parent function: vertical stretch by a factor of 2, reflection over the x-axis, horizontal translation of 3 units to
the right, and vertical translation of 4 units up.
26) Given the parent function ( ) √ write the function rule if the following transformations are done on
the parent function: vertical shrink by a factor of
, reflection over the y axis, horizontal stretch by a factor of 2,
and, and vertical translation of 3 units down.
Use your graphing calculator to solve the system of equations. Sketch the graphs, label the points of
intersection, and state the solutions. Round decimal answers to the nearest hundredth.
27) {
28) {
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
y
29) Analyze the two functions given below. Where does ( ) ( ) Explain your answer.
Solution(s):
𝒇(𝒙)
𝑥 𝑔(𝑥) -3 -11
-2 -8
-1 -5
0 -2
1 1
2 4
3 7
Solution(s):
30) The graph of the function ( ) is obtained from the graph of ( ) by shrinking the graph of ( ) vertically
by a factor of 5 and reflecting the result over the y-axis. Which of the following equations gives ( ) in terms
of ( )
A) ( ) ( )
B) ( )
( )
C) ( ) ( )
D) ( )
( )
Refer to the graph below to answer questions 31 – 33.
31) Based on the graph above, which of the following is the solution to the equation ( ) ( )
A)
B)
C)
D)
32) Based on the graph above, when is ( ) ( )
33) Based on the graph above, when is ( ) ( )
