Write your
questions here!
4.1 Transformations
PARENT FUNCTION –
TRANSLATION –
Vertical shift Horizontal shift
Given parent function
Describe translation
Given parent function
Write function with vertical shift up of 5 and
horizontal shift left of 17
SCALE –
Vertical stretch/shrink Horizontal stretch/shrink
Given parent function
Describe scale
Describe scale
Given parent function
Write function vertical shift down of 5 and
horizontal shrink by a factor of
Write function horizontal shift right of 2,
vertical shift up 3, and vertical stretch by
factor of 4
REFLECTIONS –
About x-axis About y-axis
Given parent function
Describe reflection
Describe reflection
Given parent function
Write function vertical shift up of 1 and
reflected about the x-axis
Write function horizontal shift left of 2,
vertical shrink by a factor of 5, and reflected
about y-axis
NOTES
GENERAL EQUATION OF FUNCTIONS
a =
b =
h =
k =
Quadratic Function
Cubic Function
Absolute Value Function
Square Root Function
Exponential Function
Logarithmic Function
Greatest Integer Function
Rational Function
Graph the following, use a table of values to help out if necessary.
Rules:
SUMMARY:
NOTES
𝒚
𝒂
𝒙 𝒉
𝒌
4.1 Transformations
Name the parent function. Then describe the transformation (translation, scale, and reflection) of the function
if it exists.
1.
NAME:_____________________
Translation:
Scale:
Reflection:
2.
NAME:_____________________
Translation:
Scale:
Reflection:
3.
NAME:_____________________
Translation:
Scale:
Reflection:
4.
NAME:_____________________
Translation:
Scale:
Reflection:
5.
NAME:_____________________
Translation:
Scale:
Reflection:
6.
NAME:_____________________
Translation:
Scale:
Reflection:
7.
NAME:_____________________
Translation:
Scale:
Reflection:
8.
NAME:_____________________
Translation:
Scale:
Reflection:
9.
NAME:_____________________
Translation:
Scale:
Reflection:
Given the parent function
, write the equation of the following transformation…
10. Vertical shift up 3 and horizontal
shift right 2
11. Horizontal shift left 3, vertical
stretch of 4
12. Reflect about y-axis, vertical shift
up 2, horizontal stretch of 5
Given the parent function
, write the equation of the following transformation…
13. Reflect about the x-axis,
horizontal shift right 2, vertical
shrink of ½
14. Horizontal shrink of
, vertical
shift down 6
15. horizontal shift left 4, vertical
shift down 7, horizontal stretch of 8
PRACTICE
Translation
Vertical Shift up/down ?
Horizontal Shift right/left ?
Scale
Vertical Stretch/Shrink of ?
Horizontal Stretch/Shrink of ?
Reflection
About the x-axis
About the y-axis
Given the parent function
, write the equation of the following transformation…
16. Horizontal shift left 3, reflect
about x-axis.
17. Vertical shift up 5
18. Vertical stretch 3, horizontal
shift right 5
Given the parent function
, write the equation of the following transformation…
19. Reflect about the y-axis and
horizontal shift right 8
20. Horizontal shrink of ½ and
reflect about the x-axis
21. Vertical stretch of 6, vertical shift
down 3, horizontal shift right 5,
reflect about x-axis
Given the parent function
, write the equation of the following transformation…
22. Horizontal shift right 3, vertical
shift down 5
23. Reflect about the x-axis and
vertical shift up 5
24. Vertical stretch of 5, reflect about
the y-axis, horizontal stretch of 3
The graph of a parent function and a transformation of the parent function are given. Write the equation of the
transformed function.
25.
26.
27.
Sketch a graph of the following.
28.
29.
30.
Match the function to its graph WITHOUT using a graphing calculator!
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36.
A
B
C
D
E
F
REVIEW SKILLS
Use the quadratic formula to solve. Express your solution(s) in exact and decimal form.
1.
2.
4.1 Transformations
1.
NAME:_____________________
Translation:
Scale:
Reflection:
2. Given the parent function
, write the equation
of the following transformation.
Vertical shift up 2, horizontal shift left 3,
reflect about x-axis
Describe the transformation (translation, scale, and/or reflection) that happens to the function .
3.
4.
5.
APPLICATION
Describe the transformation (translation, scale, and/or reflection) that happens to the function .
6.
7.
8.
Given the h(x) is shown below:
Sketch a graph of the following:
9.
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19.
