Transformations: Vertical and Horizontal Stretch and Shrink
Explore vertical and horizontal stretches and shrinks of functions with this comprehensive worksheet for Grade 11 math students.
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Transformations: Vertical and Horizontal Stretch and Shrink
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. A vertical stretch or shrink occurs when a function f(x) is multiplied by a constant 'a' such that the new function is g(x) = a * f(x). If |a| > 1, the graph undergoes a vertical . If 0 < |a| < 1, the graph undergoes a vertical .
2. A horizontal stretch or shrink occurs when the input 'x' of a function f(x) is multiplied by a constant 'b' such that the new function is g(x) = f(b * x). If |b| > 1, the graph undergoes a horizontal . If 0 < |b| < 1, the graph undergoes a horizontal .
3. If the graph of y = f(x) is vertically stretched by a factor of 3, the new equation is:
y = f(3x)
y = 3f(x)
y = f(x/3)
y = f(x) + 3
4. The graph of y = sin(x) is horizontally shrunk by a factor of 1/2. The new equation is:
y = 2sin(x)
y = sin(x/2)
y = sin(2x)
y = sin(x) - 2
5. Describe the transformation from the graph of f(x) to the graph of g(x) = 4f(x).
6. Describe the transformation from the graph of f(x) to the graph of h(x) = f(x/3).
7. The graph of y = x² is shown below. On the same grid, sketch the graph of y = (1/2)x².
8. The graph of y = √x is shown below. On the same grid, sketch the graph of y = √(2x).
9. A vertical stretch by a factor of 0.5 is the same as a vertical shrink by a factor of 2.
True
False
10. A horizontal shrink by a factor of 3 means replacing 'x' with '3x' in the function.
True
False