Vertical and Horizontal Transformations
Explore vertical and horizontal stretches and shrinks of functions with this Grade 12 math worksheet.
Includes
Standards
Topics
Vertical and Horizontal Transformations
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. 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
2. A horizontal shrink by a factor of 1/2 means that the new x-values are:
multiplied by 2
divided by 2
multiplied by 1/2
subtracted by 2
3. A vertical stretch by a factor of 4 transforms y = x² into y = .
4. A horizontal stretch by a factor of 2 transforms y = sin(x) into y = .
5. Describe the transformation applied to the graph of y = f(x) to obtain the graph of y = (1/2)f(x).
6. Describe the transformation applied to the graph of y = f(x) to obtain the graph of y = f(4x).
7. The graph of y = x³ is shown below. On the same grid, sketch the graph of y = 2x³.
8. The graph of y = √x is shown below. On the same grid, sketch the graph of y = √(0.5x).