Math Problem Statement
Solve
Describe how the graph of g(x) = (3√x) + 5 can be obtained from the graph of f(x) = 3√x. Then graph the function g(x).
Solution
To solve this problem, let’s break down the questions in the image:
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Transformation Question:
- The function represents a basic cubic root function.
- The function involves a vertical shift of the graph of .
- Since the transformation adds 5 to the function, it shifts the graph of 5 units up.
- This confirms that the correct answer to the transformation question is D: Shift the graph 5 units up.
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Graph Identification:
- We need to select the correct graph for .
- The transformation affects only the vertical position, so we are looking for a graph of the cubic root function that is shifted 5 units higher than the usual position of .
Upon examining the choices:
- The correct graph should resemble the cubic root shape but be visibly shifted upward.
- Based on the graphs provided, the answer should be A as it appears to have the cubic root shape shifted up by 5 units.
Summary:
- Transformation Answer: D
- Graph Identification Answer: A
Would you like a detailed explanation on why the graph shifts vertically or how to identify transformations on graphs?
Related Questions
- How does a horizontal shift affect the function ?
- What would happen if we added a negative constant to ?
- How can we determine transformations visually without calculations?
- What are some common transformations for cubic and square root functions?
- How would a reflection over the x-axis affect ?
Tip: When looking at transformations, remember that changes inside the function (like ) affect horizontal positioning, while changes outside (like ) affect vertical positioning.
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Math Problem Analysis
Mathematical Concepts
Algebra
Graph Transformations
Cube Root Functions
Formulas
g(x) = 3√x + 5
Vertical shift transformation
Theorems
Vertical transformation rule
Suitable Grade Level
Grades 9-11