Math Problem Statement
The graph shows the absolute value parent function. -5- Which statement is true? • A. The function has no intercepts. • B. (0, 0) is the x- and y-intercept of the function. • c. (0, 1) is the x- and y-intercept of the function. • D. (1, 1) is the x- and y-intercept of the function.
Solution
The absolute value parent function is defined as:
The graph of this function is a "V" shape, with the vertex at the origin, .
Analyzing the intercepts:
- X-Intercept: The x-intercept is the point where . Solving , we get .
- Y-Intercept: The y-intercept is the point where . Substituting into , we get , so the y-intercept is also .
Thus, the point is both the x- and y-intercept.
Correct Answer:
B. (0, 0) is the x- and y-intercept of the function.
Do you want further details or have any questions?
Here are 5 related questions to deepen understanding:
- What is the general form of the absolute value function, and how do transformations affect it?
- How do we determine the vertex of a transformed absolute value function?
- Can a different function have the same x- and y-intercept? Provide examples.
- What are the domain and range of the absolute value parent function?
- How do absolute value graphs differ from linear graphs?
Tip: When analyzing graphs, always check both intercepts by substituting for the y-intercept and for the x-intercept.
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Math Problem Analysis
Mathematical Concepts
Absolute Value Functions
Intercepts in Graphs
Formulas
f(x) = |x|
Theorems
Properties of the Absolute Value Parent Function
Suitable Grade Level
Grades 8-10
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