https://file.aiquickdraw.com/mathbot/file/17270533693582bma4mau.jpg

Let's examine the graph and solve the limits provided.

### Function: \( g(x) \)
We are tasked with finding the following limits based on the graph of the function \( g(x) \):

#### (a) \( \lim_{x \to -4} g(x) \)
To determine this limit, we need to analyze the behavior of \( g(x) \) as \( x \) approaches \( -4 \) from both the left and right:
- As \( x \to -4^- \) (from the left), \( g(x) \) approaches the value 2 (from below).
- As \( x \to -4^+ \) (from the right), \( g(x) \) also approaches 2.

Since both sides agree, we conclude:
\[ \lim_{x \to -4} g(x) = 2. \]

#### (b) \( \lim_{x \to -1} g(x) \)
As \( x \) approaches \( -1 \):
- From the left: \( g(x) \) approaches \( -6 \).
- From the right: \( g(x) \) also approaches \( -6 \).

Thus:
\[ \lim_{x \to -1} g(x) = -6. \]

#### (c) \( \lim_{x \to 0} g(x) \)
As \( x \) approaches \( 0 \):
- From both the left and the right, \( g(x) \) approaches \( -4 \).

So:
\[ \lim_{x \to 0} g(x) = -4. \]

#### (d) \( \lim_{x \to 0.6} g(x) \)
At \( x = 0.6 \), the function does not appear to have a defined behavior:
- The graph shows a jump discontinuity, where the value is \( -6 \) on one side and \( -4 \) on the other.

Thus, the limit does not exist:
\[ \lim_{x \to 0.6} g(x) \text{ does not exist}. \]

### Answer for part (a):
The limit is \( 2 \), so the correct choice would be option **A**.

Would you like further clarification on any step? 

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Here are 5 follow-up questions:
1. What are the conditions for a limit to exist at a point?
2. How do we interpret jump discontinuities in limit problems?
3. Can a function have a limit at a point if the function is undefined at that point?
4. What is the difference between one-sided and two-sided limits?
5. How does a removable discontinuity affect the limit at a point?

### Tip:
When analyzing limits graphically, always check both the left-hand and right-hand behavior at the point of interest.

For the function g(x) graphed here, find the following limits or state that they do not exist: a. lim g(x) as x -> -4, b. lim g(x) as x -> -1, c. lim g(x) as x -> 0, d. lim g(x) as x -> 0.6

This page guides you through finding limits from a graph of the function g(x). It includes limits at specific points, such as x = -4, x = -1, x = 0, and x = 0.6, and addresses discontinuities and limit existence conditions. Suitable for students in Grades 10-12.

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