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:

f(x)=xf(x) = |x|

The graph of this function is a "V" shape, with the vertex at the origin, (0,0)(0, 0).

Analyzing the intercepts:

  1. X-Intercept: The x-intercept is the point where f(x)=0f(x) = 0. Solving x=0|x| = 0, we get x=0x = 0.
  2. Y-Intercept: The y-intercept is the point where x=0x = 0. Substituting x=0x = 0 into f(x)=xf(x) = |x|, we get f(0)=0f(0) = 0, so the y-intercept is also (0,0)(0, 0).

Thus, the point (0,0)(0, 0) 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:

  1. What is the general form of the absolute value function, and how do transformations affect it?
  2. How do we determine the vertex of a transformed absolute value function?
  3. Can a different function have the same x- and y-intercept? Provide examples.
  4. What are the domain and range of the absolute value parent function?
  5. How do absolute value graphs differ from linear graphs?

Tip: When analyzing graphs, always check both intercepts by substituting x=0x = 0 for the y-intercept and y=0y = 0 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