Math Problem Statement
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:
-
Left Graph:
- The graph has a vertical asymptote at .
- It is undefined at , 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 , like a rational function.
-
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 .
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
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