Math Problem Statement
(f) = |x-3|-5 Write a function g whose graph is a horizontal shrink of the graph of by a factor of 1/3
Solution
To create a function from the function that represents a horizontal shrink by a factor of , we need to replace with in the original function.
Steps:
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A horizontal shrink by a factor of involves multiplying the input by the reciprocal of that factor, which is 3.
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So, replace with in the function .
Thus, the new function becomes:
This represents the horizontal shrink of the graph by a factor of .
Would you like more details or have any questions?
Here are 5 related questions for practice:
- What would the graph look like for a horizontal stretch by a factor of 2?
- How would you write a vertical shrink by a factor of ?
- What happens to the graph if we reflect across the x-axis?
- How would you translate the graph of 4 units to the right?
- What is the domain and range of ?
Tip: For horizontal transformations, always adjust the input value by multiplying inside the function.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Transformations
Formulas
g(x) = |3x - 3| - 5
Theorems
Horizontal Shrink Transformation
Suitable Grade Level
Grades 9-11
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