Transformations: Stretch and Shrink
Explore vertical and horizontal stretches and shrinks of functions with this Grade 9 math worksheet, covering coordinate plane transformations.
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Transformations: Vertical and Horizontal Stretch and Shrink
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Read each question carefully and apply your knowledge of vertical and horizontal stretches and shrinks to answer. Show all your work for short answer questions.
1. If the graph of y = f(x) is vertically stretched by a factor of 3, what is the equation of the new graph?
y = f(3x)
y = 3f(x)
y = f(x) + 3
y = f(x/3)
2. A horizontal shrink by a factor of 1/2 means that each x-coordinate is:
multiplied by 2
multiplied by 1/2
divided by 2
added to 2
1. A vertical stretch makes the graph appear (taller/shorter).
2. When a function f(x) is transformed to f(bx), if b > 1, the graph undergoes a horizontal (stretch/shrink).
3. If a graph is horizontally stretched by a factor of 4, the new x-coordinates will be the original x-coordinates.
1. Describe the transformation from f(x) to g(x) = 0.5f(x).
2. If the point (2, 4) is on the graph of y = f(x), what would be the corresponding point on the graph of y = f(2x)?
Consider the function f(x) = x². Plot the given points and then apply the specified transformation to find the new points. Sketch both the original and transformed graphs on the coordinate plane.
Original points for f(x) = x²: (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)
Transformation: Vertical stretch by a factor of 2. (i.e., g(x) = 2f(x))
1. A horizontal stretch by a factor of 3 means the graph becomes wider.
True
False
2. If 0 < a < 1, then y = af(x) represents a vertical shrink.
True
False