https://file.aiquickdraw.com/mathbot/file/1726496729667bkwcxj8z.jpg

Use the graph of the given function *f* to determine 

lim *x*→*a* *f*(*x*)

 at the indicated value of *a*, if it exists. (If an answer does not exist, enter DNE.)

From the graph provided, we need to find the limit of the function \( f(x) \) as \( x \) approaches \( a = -1 \). Let's analyze the behavior of the function near \( x = -1 \):

1. The graph shows a point at \( x = -1 \) where the function reaches a height of \( y = 3 \). Additionally, the curve is continuous on both sides of \( x = -1 \) and appears to approach this same height as \( x \) gets closer to \( -1 \) from both the left and the right.

2. Therefore, the left-hand limit (\( \lim_{x \to -1^-} f(x) \)) and the right-hand limit (\( \lim_{x \to -1^+} f(x) \)) both approach the value 3.

Since both one-sided limits are equal, the overall limit exists and is equal to the height of the function at that point.

### Answer:
\[
\lim_{x \to -1} f(x) = 3
\]

Would you like further details or have any questions?

### Related Questions:
1. What is the limit of the function as \( x \) approaches \( 3 \) in this graph?
2. How do you determine a limit when there is a discontinuity at a point?
3. What is the difference between one-sided limits and two-sided limits?
4. If the function had a jump discontinuity at \( x = -1 \), would the limit still exist?
5. How would the limit change if the point at \( x = -1 \) was an open circle at a different \( y \)-value?

### Tip:
When evaluating limits graphically, always check both the left-hand and right-hand behavior of the function around the point in question.

Use the graph of the given function f to determine lim x→a f(x) at the indicated value of a, if it exists. (If an answer does not exist, enter DNE.)

Explore how to find the limit of a function graphically as x approaches -1, covering concepts of limits and continuity. This solution uses the limit definition to find that lim x→-1 f(x) = 3, suitable for high school students in Grades 11-12.

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