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.
Includes
Standards
Topics
Transformations: Vertical and Horizontal Stretch and Shrink
Name:
Date:
Score:
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
Related Worksheets
Segment Length Practice Worksheet
Grade 11 Math worksheet focusing on calculating and applying segment lengths in various geometric contexts, including number lines, coordinate planes, and geometric figures.
Similar Figures Worksheet
This worksheet focuses on understanding and applying the properties of similar figures, including triangles and polygons, at a Grade 11 level. Students will solve problems involving scale factors, missing side lengths, and angle measures.
Secants in Circles Worksheet
Explore properties of secant lines in circles, including the Secant-Secant Theorem and tangent-secant relationships, with this Grade 11 mathematics worksheet.
Secant-Tangent Theorem Worksheet
Explore and apply the Secant-Tangent Theorem to solve for unknown lengths and angles in circles.
Triangular Prisms: Surface Area and Volume
This worksheet focuses on calculating the surface area and volume of triangular prisms, suitable for Grade 11 math students.
Triangle Sum Theorem Worksheet
A Grade 11 math worksheet focusing on the Triangle Sum Theorem, including various problem types to reinforce understanding of triangle angle properties.
Similar Solids Worksheet - Grade 11 Geometry
Explore the properties of similar solids, including their ratios of corresponding linear measures, areas, and volumes, with these challenging problems.
Eccentricity of Conic Sections
This worksheet focuses on understanding and calculating the eccentricity of conic sections, including ellipses, hyperbolas, and parabolas, for Grade 11 students.