Transformations
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Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form … and in matrix form.
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Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these … transformations with the domain of the function, and the asymptote in the graph.
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Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection … is translated.
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Reflections of a Linear Function
Explore and compare the graphs of y = f(x), y = −f(x), y = f(‑x), and y = −f(‑x), for a … linear function f(x) in slope‑intercept form. Vary the terms of f(x) and examine how the graphs change in response.
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Reflections of a Quadratic Function
Explore and compare the graphs of y = f(x), y = −f(x), y = f(−x), and y = −f(−x), for a … quadratic function f(x) of the form f(x) = ax2 + bx + c. Vary the terms of f(x) and examine how the graphs change in response.
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Rotations, Reflections and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select … different functions to translate and scale, and determine what they have in common.
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Translating and Scaling Sine and Cosine Functions - Activity A
Experiment with the graph of a sine or cosine function. Relate the values in the equation to changes in the graph, and also to terms such … as amplitude, period, and frequency.
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Translating and Scaling Sine and Cosine Functions - Activity B
Explore the graph of a sine or cosine function. Vary the terms of the equation and examine how the graph changes. Find the … amplitude, period, and frequency of the function.
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Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
