Math Problem Statement
https://mcpsmd.instructure.com/courses/858059/files/84810239/preview?verifier=jiW8HczO0HMcXefe53s3YtCjVPLLcOl6zZzK65AX Type "inf" when there is no upper bound.
Type "-inf" when there is no lower bound.
Domain: Question Blank 1 of 4 type your answer... ≤ x ≤ Question Blank 2 of 4 type your answer...
Range: Question Blank 3 of 4 type your answer... ≤ y ≤ Question Blank 4 of 4 type your answer...
Solution
The image provided shows the graph of an absolute value function, which forms a "V" shape. The turning point of the graph is at the origin (0, 0). Let's analyze the domain and range of this graph:
Domain:
The graph stretches horizontally across the entire x-axis. There are no restrictions on the values of , so the domain is all real numbers.
- Domain:
Range:
The lowest point on the graph is , and the graph extends upward indefinitely. Therefore, the range starts at 0 and goes to infinity.
- Range:
Final answers for the blanks:
- Domain:
- Blank 1: "-inf"
- Blank 2: "inf"
- Range:
- Blank 3: "0"
- Blank 4: "inf"
Would you like further details on how to analyze such functions?
Here are 5 related questions for further exploration:
- What is the equation of the absolute value function in this graph?
- How do you find the vertex of an absolute value function graph?
- What is the slope of the lines on either side of the vertex?
- How does the graph of an absolute value function change when the function is shifted horizontally or vertically?
- Can the range of an absolute value function ever include negative numbers?
Tip: The domain of absolute value functions is always all real numbers, but the range is limited by the vertex and direction of the "V" shape.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Absolute Value Functions
Formulas
y = |x|
Theorems
Properties of Absolute Value Functions
Suitable Grade Level
Grades 7-10