Math Problem Statement
Answer each of the following questions about the graph for
y=4/11|x-7|-2
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Does the graph open up or down? Select an answer
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Give the vertex as an ordered pair.
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Is this point the maximum or minimum of the graph? Select an answer
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Is the graph wider, narrower, or the same width as the parent function ? Select an answer
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From the parent fucntion this graph has been shift horizontally ? unit(s) to the Select an answer
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From the parent function this graph has been shifted vertically ? unit(s) Select an answer .
Solution
Let's break down the equation step by step:
Given equation:
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Does the graph open up or down?
- The coefficient of the absolute value function, , is positive. This means the graph opens up.
Answer: The graph opens up.
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Give the vertex as an ordered pair.
- The general form of the absolute value function is , where the vertex is at .
- In this case, the vertex is at .
Answer: The vertex is .
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Is this point the maximum or minimum of the graph?
- Since the graph opens upwards, the vertex represents the minimum point of the graph.
Answer: This point is the minimum.
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Is the graph wider, narrower, or the same width as the parent function ?
- The coefficient is less than 1, which means the graph is wider than the parent function.
Answer: The graph is wider.
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From the parent function , this graph has been shifted horizontally how many unit(s) to the left or right?
- The term indicates a horizontal shift 7 units to the right.
Answer: 7 units to the right.
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From the parent function , this graph has been shifted vertically how many unit(s)?
- The outside the absolute value indicates a vertical shift 2 units down.
Answer: 2 units down.
Relative Questions:
- How would the graph change if the coefficient of the absolute value were negative?
- What is the effect of increasing the coefficient of ?
- How does the vertex form help identify transformations of the parent function?
- If the horizontal shift were 5 units to the left, what would the equation look like?
- How would the graph change if the vertical shift was 3 units up?
Tip:
When dealing with absolute value functions, always check the sign of the coefficient in front of the absolute value to determine the direction of the opening.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Functions
Graph Transformations
Formulas
y = a|x - h| + k (Vertex Form)
Transformation: Vertical and Horizontal Shifts
Width change based on coefficient
Theorems
Graph transformation rules for absolute value functions
Vertex determination from the equation
Suitable Grade Level
Grades 9-11