Math Problem Statement

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Consider the function graph here: A) The vertical asymptote(s) are:

Solution

To solve this problem, we need to determine the vertical asymptote(s) based on the graph.

Analyzing the Graph:

The function appears to have two vertical asymptotes, which occur where the graph approaches infinity or negative infinity, and the function is undefined.

From the graph, we can observe:

  • There is a vertical asymptote at x=2x = -2.
  • There is another vertical asymptote at x=2x = 2.

Thus, the vertical asymptotes are at: x=2 and x=2\boxed{x = -2 \text{ and } x = 2}

Would you like more details on how to identify vertical asymptotes, or do you have any further questions?

Here are 5 related questions:

  1. How do you identify horizontal asymptotes in a graph?
  2. Can a graph have more than two vertical asymptotes?
  3. What is the behavior of a function near a vertical asymptote?
  4. How can we find vertical asymptotes algebraically from a function?
  5. What is the difference between a hole in the graph and a vertical asymptote?

Tip: Vertical asymptotes occur where the denominator of a rational function equals zero and the numerator is non-zero.

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Math Problem Analysis

Mathematical Concepts

Vertical Asymptotes
Graph Analysis
Limits

Formulas

Vertical asymptotes occur where the denominator of a rational function equals zero, and the numerator is non-zero.

Theorems

Vertical Asymptote Theorem

Suitable Grade Level

Grades 9-12