Math Problem Statement
Solution
We are tasked with analyzing the graph of the function using transformations of the basic square root function .
Let's break down the transformations in :
-
Horizontal Shift: The term indicates a horizontal shift. The graph of will shift to the right by 5 units because the general form of a horizontal shift is , which shifts the graph right by units.
-
Vertical Stretch/Shrink: The coefficient outside the square root indicates a vertical shrink. A number less than 1 (in absolute value) multiplies the output of the function, thus compressing the graph vertically.
Combining both transformations:
- A horizontal shift to the right by 5 units.
- A vertical shrink by a factor of .
Now, let's review the multiple-choice answers:
- Option A: Horizontal shift left by 5 units and horizontal stretch by – Incorrect.
- Option B: Horizontal shift right by 5 units and vertical shrink by – Correct.
- Option C: Horizontal shift left by 5 units and vertical shrink by – Incorrect.
- Option D: Horizontal shift right by 5 units and horizontal stretch by – Incorrect.
Correct Answer: B.
Would you like further details on how these transformations affect the graph? Here are some related questions to consider:
- How do horizontal shifts impact the graph of any function?
- What is the effect of vertical stretches and shrinks on a graph?
- How would the graph change if the coefficient was negative?
- Can you explain the difference between horizontal and vertical transformations?
- How do transformations differ for other types of functions, like quadratics?
Tip: When analyzing transformations, always address horizontal and vertical changes separately for clarity.
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Math Problem Analysis
Mathematical Concepts
Functions
Transformations
Square Root Functions
Formulas
g(x) = 1/3 √(x - 5)
Theorems
Transformation rules for functions
Horizontal and vertical shifts
Suitable Grade Level
Grades 9-11
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