| Describing Basic Transformations | Describing Multi-Step Transformations | Writing Transformations | Vocabulary |
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The graph of g is a vertical translation 3 units down of the graph of f.
Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
f(x) = 1/3x + 3 g(x) = f(x) - 3 |
The transformations are a vertical shrink by a factor of 1/3 then a vertical translation 1 unit up.
Describe the transformations from the graph of f to the graph of h.
f(x) = x h(x) = 1/3x + 1 |
g(x) = f(x - 2)
Write a function g in terms of f so that the statement is true.
The graph of g is a horizontal translation 2 units right of the graph of f. |
What is a transformation?
Changes the size, shape, position, or orientation of a graph.
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The graph of g is a horizontal translation 3 units right of the graph of f.
Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
f(x) = 1/2x - 5 g(x) = f(x - 3) |
The transformations are a vertical stretch by a factor of 4 then a vertical translation 2 units down.
Describe the transformations from the graph of f to the graph of h.
f(x) = x h(x) = 4x - 2 |
g(x) = f(-x)
Write a function g in terms of f so that the statement is true.
The graph of g is a reflection in the y-axis of the graph of f. |
What is a translation?
A transformation that shifts a graph horizontally or vertically but does not change the size, shape, or orientation of the graph.
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The graph of h is a reflection in the y-axis of the graph of f.
Use the graphs of f and h to describe the transformation from the graph of f to the graph of h.
f(x) = -5 - x h(x) = f(-x) |
The transformations are a vertical shrink by a factor of 1/2, then a reflection in the x-axis, then a vertical translation 3 units up.
Describe the transformations from the graph of f to the graph of h.
f(x) = x h(x) = -1/2x + 3 |
g(x) = 4f(x)
Write a function g in terms of f so that the statement is true.
The graph of g is a vertical stretch by a factor of 4 of the graph of f. |
What is a reflection?
A transformation that flips a graph over a line called the line of reflection.
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The graph of r is a horizontal stretch of the graph of f by a factor of 2.
Use the graphs of f and r to describe the transformation from the graph of f to the graph of r.
f(x) = -2x - 4 r(x) = f(1/2x) |
The transformations are a reflection in the x-axis then a vertical translation 7 units down.
Describe the transformations from the graph of f to the graph of h.
f(x) = 3x h(x) = -3x - 7 |
g(x) = f(5x)
The graph of g is a horizontal shrink by a factor of 1/5 of the graph of f.
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What is a horizontal shrink or stretch?
Transforming a function by multiplying all the x-coordinates (inputs) by the same factor a.
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The graph of h is a vertical shrink of the graph of f by a factor of 1/6.
Use the graphs of f and h to describe the transformation from the graph of f to the graph of h.
f(x) = 3x - 12 h(x) = 1/6f(x) |
The transformations are a vertical stretch by a factor of 3 then a vertical translation 5 units down.
Describe the transformations from the graph of f to the graph of h.
f(x) = 2x h(x) = 6x - 5 |
g(x) = 1/6f(x)
The graph of g is a vertical shrink by a factor of 1/6 of the graph of f.
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What is a vertical shrink or stretch?
Transforming a function by multiplying all the y-coordinates (outputs) by the same factor a.
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