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Combining Transformations

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Wize High School Grade 12 Pre-Calculus Textbook > Transformations

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Combining Transformations

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Practice: Combining Transformations

Sketch y=−12(13x+2)2−1y=-\frac{1}{2}\Big(\frac{1}{3}x+2\Big)^2-1.
More Combining Transformations Questions:
Transformations
Match the transformation with the correct statement.
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
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
Match the transformation with the correct statement.
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
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
Match the transformation with the correct statement.
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
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.