Math Problem Statement

The graphs of two parent functions are shown. Which answer functions are they? Choose all that apply: A) Square Root, B) Absolute Value, C) Exponential, D) Logarithmic, E) Rational.

Solution

The image shows two graphs, each representing a piecewise function. The task is to identify which answer describes the given graphs, with options provided as follows:

  • A) Square Root
  • B) Absolute Value
  • C) Exponential
  • D) Logarithmic
  • E) Rational

Let's analyze the graphs to determine the correct answer:

  1. Left Graph:

    • The graph has a vertical asymptote at x=0x = 0.
    • It is undefined at x=0x = 0, and the graph appears in two separate parts: one in the first quadrant and one in the third quadrant.
    • This suggests that the function might be of a form that involves division by xx, like a rational function.
  2. Right Graph:

    • The graph is V-shaped and symmetric with respect to the y-axis.
    • This is characteristic of the absolute value function, which has the general form y=xy = |x|.

Given these observations:

  • The first graph corresponds to a rational function.
  • The second graph corresponds to an absolute value function.

Thus, the answer would be B) Absolute Value and E) Rational.

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Math Problem Analysis

Mathematical Concepts

Algebra
Piecewise Functions
Graph Analysis

Formulas

y = |x|
y = 1/x

Theorems

Properties of Absolute Value Functions
Properties of Rational Functions

Suitable Grade Level

Grades 9-12