5/20/25, 8:59 PM
Alef Frontend
View hints
View feedback
Play All
Question 1
Write an equation for the function whose graph is obtained from the graph of the parent function
y=
x
after a translation of 6 units up.
Write your answer in the space provided.
x +6
y=
Question 2
Write an equation for the function whose graph is obtained from the graph of the parent function
y=
x
after a translation of 6 units down.
Write your answer in the space provided.
y=
x −6
Question 3
Which graph shows the parent graph of
y=
x
and the transformed graph of
y=
1
3
x
?
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
1/36
5/20/25, 8:59 PM
Alef Frontend
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
2/36
5/20/25, 8:59 PM
Alef Frontend
Question 4
Find the domain and range of the function
y=
1
4
x −7
.
Drag and drop each correct answer into the appropriate box.
Domain: all real numbers x, such that x
≥0
Range: all real numbers y, such that y
≥ −7
≤
1
4
.
.
≥7
≤7
≥
1
4
≤0
Question 5
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
3/36
5/20/25, 8:59 PM
Alef Frontend
For the function
y=−
x +8 −7
, describe the transformations of the graph of the function from the parent graph.
Select from the drop-down menus to correctly complete each statement.
Use the form
y =a
x −h +k
.
The graph of the function will be translated
8
units to the left because
a = −1
.
units down because
k = −7
The graph of the function will be reflected over the x-axis , because
The graph of the function will be translated
7
h = −8
.
.
Question 6
Which of these are transformations of the graph of
y = 2 x −6 +1
from the parent graph
y=
x
?
vertical stretch
translation 6 units left
translation down 1 unit
translation 6 units right
vertical compression
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
4/36
5/20/25, 8:59 PM
Alef Frontend
translation up 1 unit
Question 7
What is the domain and range of the function
y = 4 x +1 −2
?
The domain is all real numbers, such that
The range is all real numbers, such that
x ≥ −1
y ≥ −2
.
.
Question 8
Look at the graph. The parent graph,
y=
x
, has been vertically stretched by a factor of 3.
It has also been translated horizontally and vertically.
The function is
y =3
x −4 +1
.
Write it in the form
y =a
x −h +k
. You have already been given the value of
a
, which is 3.
Question 9
Drag and drop the correct equation into the box.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
5/36
5/20/25, 8:59 PM
Alef Frontend
The functions
y=
x
and
y=
x −4
are graphed on the coordinate plane.
y = −4 x
y=
y = 4−
x
x −4
Question 10
Consider the parent function
y=
x
and the transformed function
y=
x −3
.
Write your answers in the spaces provided.
Find the domain and range of the transformed function.
Domain: All real numbers x, such that
x≥
0
Range: All real numbers y such that
y≥
-3
.
Question 11
Write an equation for the function whose graph is obtained from the graph of the parent function
y=
x
after a translation of 6 units to the right.
Write your answer in the space provided.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
6/36
5/20/25, 8:59 PM
Alef Frontend
y=
x −6
Question 12
What is the domain and range of the function
y = −3 x +1 −5
?
The domain is all real numbers x, such that
x≥1
.
The range is all real numbers y, such that
y ≤ −5
.
The domain is all real numbers x, such that
x ≥ −1
.
The range is all real numbers y, such that
y ≥ −5
.
The domain is all real numbers x, such that
x ≥ −1
.
The range is all real numbers y, such that
y ≤ −5
.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
7/36
5/20/25, 8:59 PM
Alef Frontend
The domain is all real numbers x, such that
x≥1
.
The range is all real numbers y, such that
y ≥ −5
.
Question 13
What is the domain and range of the function
y = 2 x −4 +1
?
The domain is all real numbers x, such that
x ≤ −4
.
The range is all real numbers y, such that
y≥1
.
The domain is all real numbers x, such that
x ≥ −4
.
The range is all real numbers y, such that
y≤1
.
The domain is all real numbers x, such that
x≤4
.
The range is all real numbers y, such that
y ≥ −1
.
The domain is all real numbers x, such that
x≥4
.
The range is all real numbers y, such that
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
8/36
5/20/25, 8:59 PM
Alef Frontend
y≥1
.
Question 14
The parent function
y=
x
and a transformed function are graphed on the coordinate plane.
Drag and drop the correct equation into the box.
The equation describing the transformed function is
y = −2 x
y = −2 x
y=
x −2
.
y =2 x
Question 15
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749-…
9/36
5/20/25, 8:59 PM
Alef Frontend
What function is graphed on the coordinate plane?
y=
1
3
x +3 −4
y=
1
3
x −3 −4
y=−
1
3
x −3 −4
y=−
1
3
x +3 −4
Question 16
What are the equations of the functions graphed on the coordinate plane?
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
10/36
5/20/25, 8:59 PM
Alef Frontend
y = −6 x
y =6 x
y=−
1
6
y=
x
x
1
6
x
y=−
x
y=
Question 17
Consider the parent function
y=
x
and a transformed function in the form
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
11/36
5/20/25, 8:59 PM
y=
Alef Frontend
x +k
, where k is a positive real number.
Select the values that could be included in the range of the transformed function.
–k
k +2
k
–4
0
–2
Question 18
Consider the function
y=
x +7
, transformed from the parent function
y=
x
.
Drag and drop each correct answer into the appropriate box.
The domain of the transformed function is all real numbers x, such that
The range of the transformed function is all real numbers y, such that
y ≤ −7
y ≥ −7
x ≥ −7
y≥0
x ≤ −7
.
.
x≥7
x≥0
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
12/36
5/20/25, 8:59 PM
Alef Frontend
Question 19
The parent function
y=
x
and the transformed function
y = −3 x
are graphed on the coordinate plane.
Select the numbers that appear in the domain of the transformed
function.
–1
–9
–2
0
3
–3
Question 20
Look at the graph. The parent graph
y=
x
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
13/36
5/20/25, 8:59 PM
Alef Frontend
has been vertically stretched.
It has also been translated horizontally and/or vertically.
Choose the correct function for the graph on the coordinate plane.
y = −2 x −3
y = −2 x +3
y = −2 x −3
y = −2 x +3
Question 21
Describe the transformations from the graph of f(x) to the graph of g(x).
f (x ) =
x
g (x ) =
x +7
The graph of f(x) translated 7 units to the right
The graph of f(x) translated 7 units up
The graph of f(x) translated 7 units down
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
14/36
5/20/25, 8:59 PM
Alef Frontend
The graph of f(x) translated 7 units to the left
Question 22
Drag and drop the correct answer into the appropriate box.
f (x ) =
x
1
g (x ) =
x
4
The graph of g(x) is a vertical compression
of the graph of f(x).
reflection
stretch
shift
Question 23
Choose the equation that represents the blue graph, given the parent graph
y=
x
.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
15/36
5/20/25, 8:59 PM
Alef Frontend
y=
4x
y=
x −4
y=
x +4
y =4 x
Question 24
The graph of the function
y=−
1
3
x
is the graph of the function
y=
x
transformed in which way?
reflected across the x-axis and vertically compressed
reflected across the y-axis and vertically stretched
reflected across the y-axis and vertically compressed
reflected across the x-axis and vertically stretched
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
16/36
5/20/25, 8:59 PM
Alef Frontend
Question 25
Which of these are transformations of the graph of
y = −0.5 x +2 +4
from the parent graph
y=
x
?
translation 2 units up
reflection across the y-axis
translation 4 units down
vertical stretch
translation 2 units left
translation 4 units up
translation 2 units right
vertical compression
Question 26
Select the equations that represent the graphs of the parent function and the transformed function graphed on the coordinate
plane.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
17/36
5/20/25, 8:59 PM
Alef Frontend
y =2 x
y=
x
2
y =4 x
y=
x
4
y=
x
y=
x +2
Question 27
Choose the set of equations that represents the parent function and transformed function graphed on the coordinate plane.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
18/36
5/20/25, 8:59 PM
Alef Frontend
y=
x
and
y=−
1
2
y=
x
x
and
y=−
1
4
y=
x
x
and
y = −2 x
y=
x
and
y = −4 x
Question 28
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
19/36
5/20/25, 8:59 PM
Alef Frontend
Select from the drop-down menus to correctly complete the sentence.
The graph of the function
y=
x −5
is the graph of the function
y=
x
translated
vertically
down 5 units
.
Question 29
The graph of the function
y=
x +3
is the graph of
y=
x
transformed in which way?
translated horizontally 3 units to the left
translated vertically 3 units up
translated vertically 3 units down
translated horizontally 3 units to the right
Question 30
The function
y=
x
and a transformed function in the form
y=
x −h
are graphed on the coordinate plane.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
20/36
5/20/25, 8:59 PM
Alef Frontend
Which statement about the value of h is correct?
h>0
h=0
h <0
0<h<1
Question 31
The function
y=
x
and a transformed function in the form
y=
x −h
are graphed on the coordinate plane.
Which statement about the value of h is correct?
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
21/36
5/20/25, 8:59 PM
Alef Frontend
0<h<1
h>0
h<0
h=0
Question 32
The parent function
y=
x
and a transformed function in the form
y =a
x
are graphed on the coordinate plane.
Which statement about the value of a is correct?
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
22/36
5/20/25, 8:59 PM
Alef Frontend
a<0
a =1
a>1
0<a <1
Question 33
Choose the set of equations that represents the graphs of the parent function and transformed function graphed on the
coordinate plane.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
23/36
5/20/25, 8:59 PM
Alef Frontend
y=
x
and
y =5 x
y=
x
and
y=
x
5
y=
x
and
y=
x +5
y=
x
and
y=
x −5
Question 34
The parent function
y=
x
and a transformed function in the form
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
24/36
5/20/25, 8:59 PM
y =a
Alef Frontend
x
are graphed on the coordinate plane.
Which statement is correct about the value of a?
a<0
a>1
0<a <1
a =1
Question 35
Choose the set of equations that represents the parent function and transformed function graphed on the coordinate plane.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
25/36
5/20/25, 8:59 PM
Alef Frontend
y=
x
and
y=
x −5
y=
x
and
y=
x −5
y=
x
and
y=
x +5
y=
x
and
y=
x +5
Question 36
Select from the drop-down menu to correctly complete the sentence.
The graph of
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
26/36
5/20/25, 8:59 PM
Alef Frontend
g (x ) = 4 x
is a vertical
stretch
f (x ) =
x
of the graph of
.
Question 37
Consider the function
y=−
x −3 +2
. Describe the transformations of the graph of the function from the parent graph.
Select from the drop-down menus to correctly complete each statement.
Use the form
y =a
x −h +k
.
The graph of the function will be translated
right
3 units, because h =
3
–1
.
The graph of the function will be reflected over the x-axis, because a =
The graph of the function will be translated
up
.
2 units, because k = 2.
Question 38
Complete the table of values for the parent function
y=
x
and transformed function
y=
x +2
.
Drag and drop each correct value into the appropriate box.
x
0
1
4
9
16
25
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
27/36
5/20/25, 8:59 PM
Alef Frontend
y=
x
0
y=
x +2
2
1
3
2
2
3
4
5
5
4
5
7
6
8
6
0
Question 39
Select all the numbers in the domain of both the parent function
y=
x
and the transformed function
y=
x −8
.
6
12
0
4
–1
1
9
8
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
28/36
5/20/25, 8:59 PM
Alef Frontend
–2
Question 40
What function is graphed on the coordinate plane?
y=
x +5 −5
y=−
x −5
y=
x −5
y = −2 x +5
Question 41
Write an equation for the function whose graph is obtained from the graph of the parent function
y=
x
after a translation of 6 units to the left.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
29/36
5/20/25, 8:59 PM
Alef Frontend
Write your answer in the space provided.
y=
x +6
Question 42
Write an equation for the function whose graph is obtained from the graph of the parent function
y=
x
after a translation of 10 units up.
Write your answer in the space provided.
y=
x + 10
Question 43
Describe the transformations from the graph of f(x) to the graph of g(x).
f (x ) =
x
g (x ) =
x −3
The graph f(x) translated 3 units down.
The graph f(x) translated 3 units up.
The graph f(x) translated 3 units to the right.
The graph f(x) translated 3 units to the left.
Question 44
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
30/36
5/20/25, 8:59 PM
Alef Frontend
What function is graphed on the coordinate plane?
y=−
y=
x +2 −3
x −2 −3
y=−
y=
x +3 −2
x −3 −2
Question 45
Select the domain and range of both graphs.
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
31/36
5/20/25, 8:59 PM
Alef Frontend
all real numbers x, such that
x>0
all real numbers y, such that
0 ≤ y ≤ 10
all real numbers x, such that
0 ≤ x ≤ 10
all real numbers x, such that
x≥0
all real numbers y, such that
y>0
all real numbers y, such that
y≥0
Question 46
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
32/36
5/20/25, 8:59 PM
Alef Frontend
Which graph represents the function
y=−
1
2
x −1 +3
?
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
33/36
5/20/25, 8:59 PM
Alef Frontend
Question 47
Consider the function
y=
x +5
, transformed from the parent function
y=
x
.
Select from the drop-down menus to correctly complete the sentences.
The domain of the function
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
34/36
5/20/25, 8:59 PM
y=
Alef Frontend
x +5
is all real numbers x, such that
x ≥ −5
.
The range of the function
y=
x +5
is all real numbers y, such that
y≥0
.
Question 48
Look at the graph. The parent graph
y=
x
has been vertically stretched.
It has also been translated horizontally and vertically.
Choose the correct function for the graph on the coordinate plane.
y = 2 x −4 +5
y = 2 x +4 −5
y = 2 x +4 +5
y = 2 x −4 −5
Question 49
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
35/36
5/20/25, 8:59 PM
Alef Frontend
A function is transformed from the parent function
y=
x
by a vertical translation of 2.5 units down. Which equation represents the transformed function?
y=
x −2.5
y=
x +2.5
y=
2.5−x
y=
x −2.5
Question 50
The graph of
y = −2 x
is the graph of
y=
x
transformed in which way?
reflected across the x-axis and vertically compressed
reflected across the x-axis and vertically stretched
reflected across the y-axis and vertically compressed
reflected across the y-axis and vertically stretched
https://moe.alefed.com/teacher/?1747758011389#/activityConfig/preview/contentId/c6c38151-3033-41dc-89bf-fe0af0aa0ae2/classId/a85179f8-7749…
36/36