https://file.aiquickdraw.com/mathbot/file/1726798260029d8bzvbni.jpg

https://file.aiquickdraw.com/mathbot/file/1726798260029j438n2pk.jpg

From the graph you have provided, we can identify the types of discontinuities at the given \( x \)-values by analyzing the behavior of the function at each point. Let's go through them one by one based on the first image:

1. **At \( x = -4 \):**
   The function shows a **removable discontinuity**. This is indicated by a hole in the graph, meaning the limit exists at \( x = -4 \), but the function is not defined at that point or defined at a different value than the limit.

2. **At \( x = -2 \):**
   The function exhibits a **jump discontinuity**. This is seen as the graph jumps from one point to another without connecting. The left-hand and right-hand limits exist but are not equal.

3. **At \( x = 2 \):**
   The function has a **removable discontinuity**. There is a hole at this point, similar to \( x = -4 \), meaning the function is not defined at \( x = 2 \), though the limit exists.

4. **At \( x = 4 \):**
   This shows an **infinite discontinuity**. The graph approaches infinity as \( x \) nears 4 from the left, while from the right, it drops towards negative infinity, creating a vertical asymptote.

Would you like more details or further explanations on any of these types of discontinuities? Here are 5 related

What type of discontinuity does the function f have at x = -4, x = -2, x = 2, and x = 4?

Analyze the graph of a function to determine the types of discontinuities at x = -4, x = -2, x = 2, and x = 4. The problem involves identifying removable, jump, and infinite discontinuities using graph analysis. Suitable for high school students.

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