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Transformations

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Wize High School Grade 12 Pre-Calculus Textbook > Transformations

Combining Transformations

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Wize High School Grade 11 Math Textbook > Transformations of Functions

Combining Transformations

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Wize High School Algebra II Textbook (Common Core) > Transformations of Functions

Combining Transformations

6 Activities

Match the transformation with the correct statement.
A.
f(x)  →  f(x−2)f(x)~~{\color{red}\rightarrow}~~f(x-2)
B.
f(x)  →  f(x+3)−5f(x)~~{\color{red}\rightarrow}~~f(x+3)-5
C.
f(x)  →  −f(−x)f(x)~~{\color{red}\rightarrow}~~-f(-x)
D.
f(x)  →  −f(12x−8)f(x)~~{\color{red}\rightarrow}~~-f\Bigg(\dfrac{1}{2}x-8\Bigg)
E.
f(x)  →  3f(3(x+2))+2f(x)~~{\color{red}\rightarrow}~~3f(3(x+2))+2
F.
f(x)  →  f(−2x+8)f(x)~~{\color{red}\rightarrow}~~f(-2x+8)
Horizontal reflection about the y-axis and vertical reflection about the x-axis.
Horizontal translation 2 units right.
Horizontal translation 3 units left and vertical translation 5 units left.
Horizontal reflection about the y-axis, horizontal compression by a factor of 12\dfrac{1}{2}, and a horizontal translation 4 units right.
Vertical reflection about the x-axis, horizontal expansion by a factor of 2, and a horizontal translation 16 units right.

Horizontal compression by a factor of 13\dfrac{1}{3}, horizontal translation 2 units left, vertical expansion by a factor of 3, and a vertical translation 2 units up.
More Combining Transformations Questions:
Transformations
Let f(x)f(x) and its table of values be shown below.
xy−210−31−24−88092\begin{array}{|c|c|}\hline x&y\\\hline -2&1\\\hline 0&-3\\\hline 1&-2\\\hline 4&-8\\\hline 8&0\\\hline 9&2\\\hline \end{array}
Combining Transformations
Practice: Combining Transformations
If the point (6,−4) (6, -4)~ is on the graph of the function y=−4f(−5x+1)−2y=-4f(-5x+1)-2, then what point must be on the graph of the function y=f(x)?y=f(x)?
Combining Transformations
Practice: Combining Transformations
Sketch y=−12(13x+2)2−1y=-\frac{1}{2}\Big(\frac{1}{3}x+2\Big)^2-1.
Combining Transformations
The following table of values is for the function y=f(x):y=f(x):
xy−810−67.5−45−36−210\begin{array}{|c|c|} \hline x&y\\\hline -8&10\\\hline -6&7.5\\\hline -4&5\\\hline -3&6\\\hline -2&10\\\hline \end{array}
Which of the following is a table of values for y=2f(−12(x−1))+1y=2f(-\frac{1}{2}(x-1))+1?
Transformations
Let y=2f(x−1)y=2f(x-1)be shown below along with the table of values.
x2f(x−1)−5−20−2103446\begin{array}{|c|c|}\hline x&2f(x-1)\\\hline -5&-2\\\hline 0&-2\\\hline 1&0\\\hline 3&4\\\hline 4&6\\\hline \end{array}
Find the table of values for y=2f(2x+2)−1y=2f(2x+2)-1.
Transformations
Let (a,b)(a,b) be on the graph of the function 2y=f(0.25x−1.25)+22y=f(0.25x-1.25)+2. What point must be on the following?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The function y=−22x+3y=-2\sqrt{2x+3} has been vertically translated 3 units down and horizontally translated 4 units right.
Write the equation of the transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The function y=2f(x−2)+3y=2f(x-2)+3 has been vertically reflected about the x-axis, vertically translated 5 units down, horizontally translated 8 units left.
Write the equation of the transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
If y=f(x) y=f(x)~ is shown below,
which of the following is the transformation y=−2f(x−3)+1y=-2f(x-3)+1?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
If y=f(x) y=f(x)~ is shown below,
which of the following is the transformation y=−f(x+1)?y=-f(x+1)?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The point (a, b) is on the graph of y=f(x).y=f(x).
Match the point to the appropriate transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The point (-2, 5) is on the graph of y=f(x).y=f(x).
Match the point to the appropriate transformed function.
More Combining Transformations Questions:
Transformations
Let f(x)f(x) and its table of values be shown below.
xy−210−31−24−88092\begin{array}{|c|c|}\hline x&y\\\hline -2&1\\\hline 0&-3\\\hline 1&-2\\\hline 4&-8\\\hline 8&0\\\hline 9&2\\\hline \end{array}
Combining Transformations
Practice: Combining Transformations
If the point (6,−4) (6, -4)~ is on the graph of the function y=−4f(−5x+1)−2y=-4f(-5x+1)-2, then what point must be on the graph of the function y=f(x)?y=f(x)?
Combining Transformations
Practice: Combining Transformations
Sketch y=−12(13x+2)2−1y=-\frac{1}{2}\Big(\frac{1}{3}x+2\Big)^2-1.
Combining Transformations
The following table of values is for the function y=f(x):y=f(x):
xy−810−67.5−45−36−210\begin{array}{|c|c|} \hline x&y\\\hline -8&10\\\hline -6&7.5\\\hline -4&5\\\hline -3&6\\\hline -2&10\\\hline \end{array}
Which of the following is a table of values for y=2f(−12(x−1))+1y=2f(-\frac{1}{2}(x-1))+1?
Transformations
Let y=2f(x−1)y=2f(x-1)be shown below along with the table of values.
x2f(x−1)−5−20−2103446\begin{array}{|c|c|}\hline x&2f(x-1)\\\hline -5&-2\\\hline 0&-2\\\hline 1&0\\\hline 3&4\\\hline 4&6\\\hline \end{array}
Find the table of values for y=2f(2x+2)−1y=2f(2x+2)-1.
Transformations
Let (a,b)(a,b) be on the graph of the function 2y=f(0.25x−1.25)+22y=f(0.25x-1.25)+2. What point must be on the following?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The function y=−22x+3y=-2\sqrt{2x+3} has been vertically translated 3 units down and horizontally translated 4 units right.
Write the equation of the transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The function y=2f(x−2)+3y=2f(x-2)+3 has been vertically reflected about the x-axis, vertically translated 5 units down, horizontally translated 8 units left.
Write the equation of the transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
If y=f(x) y=f(x)~ is shown below,
which of the following is the transformation y=−2f(x−3)+1y=-2f(x-3)+1?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
If y=f(x) y=f(x)~ is shown below,
which of the following is the transformation y=−f(x+1)?y=-f(x+1)?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The point (a, b) is on the graph of y=f(x).y=f(x).
Match the point to the appropriate transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The point (-2, 5) is on the graph of y=f(x).y=f(x).
Match the point to the appropriate transformed function.
More Combining Transformations Questions:
Transformations
Let f(x)f(x) and its table of values be shown below.
xy−210−31−24−88092\begin{array}{|c|c|}\hline x&y\\\hline -2&1\\\hline 0&-3\\\hline 1&-2\\\hline 4&-8\\\hline 8&0\\\hline 9&2\\\hline \end{array}
Combining Transformations
Practice: Combining Transformations
If the point (6,−4) (6, -4)~ is on the graph of the function y=−4f(−5x+1)−2y=-4f(-5x+1)-2, then what point must be on the graph of the function y=f(x)?y=f(x)?
Combining Transformations
Practice: Combining Transformations
Sketch y=−12(13x+2)2−1y=-\frac{1}{2}\Big(\frac{1}{3}x+2\Big)^2-1.
Combining Transformations
The following table of values is for the function y=f(x):y=f(x):
xy−810−67.5−45−36−210\begin{array}{|c|c|} \hline x&y\\\hline -8&10\\\hline -6&7.5\\\hline -4&5\\\hline -3&6\\\hline -2&10\\\hline \end{array}
Which of the following is a table of values for y=2f(−12(x−1))+1y=2f(-\frac{1}{2}(x-1))+1?
Transformations
Let y=2f(x−1)y=2f(x-1)be shown below along with the table of values.
x2f(x−1)−5−20−2103446\begin{array}{|c|c|}\hline x&2f(x-1)\\\hline -5&-2\\\hline 0&-2\\\hline 1&0\\\hline 3&4\\\hline 4&6\\\hline \end{array}
Find the table of values for y=2f(2x+2)−1y=2f(2x+2)-1.
Transformations
Let (a,b)(a,b) be on the graph of the function 2y=f(0.25x−1.25)+22y=f(0.25x-1.25)+2. What point must be on the following?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The function y=−22x+3y=-2\sqrt{2x+3} has been vertically translated 3 units down and horizontally translated 4 units right.
Write the equation of the transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The function y=2f(x−2)+3y=2f(x-2)+3 has been vertically reflected about the x-axis, vertically translated 5 units down, horizontally translated 8 units left.
Write the equation of the transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
If y=f(x) y=f(x)~ is shown below,
which of the following is the transformation y=−2f(x−3)+1y=-2f(x-3)+1?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
If y=f(x) y=f(x)~ is shown below,
which of the following is the transformation y=−f(x+1)?y=-f(x+1)?
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The point (a, b) is on the graph of y=f(x).y=f(x).
Match the point to the appropriate transformed function.
Vertical & Horizontal Reflections
Practice: Vertical & Horizontal Reflections
The point (-2, 5) is on the graph of y=f(x).y=f(x).
Match the point to the appropriate transformed function.