https://file.aiquickdraw.com/mathbot/file/1727216945701ma456h5i.jpg

(e)    
lim 
x → 4 
f(x)

 
Incorrect: Your answer is incorrect.


(f)    
f(4)



Let's analyze the graph you provided to answer the two parts (e) and (f):

### (e) \(\lim_{x \to 4} f(x)\):
This question asks for the limit of \(f(x)\) as \(x\) approaches 4. Looking at the graph near \(x = 4\), the function appears to approach a value close to \(3\). Therefore, we can estimate:

\[
\lim_{x \to 4} f(x) = 3.
\]

### (f) \(f(4)\):
This part asks for the value of the function at \(x = 4\). From the graph, we can see that there is a small open circle at \(x = 4\), which means that the function is not defined at this point.

Thus, we conclude:
\[
f(4) \text{ is undefined.}
\]

Let me know if you want further details, or if you have any other questions!

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Here are 5 related questions:
1. What is the difference between a limit and the function value at a point?
2. How do you determine whether a function is continuous at a point?
3. Can a function have a limit at a point where it is not defined?
4. What are removable and non-removable discontinuities in a graph?
5. How do we analyze the behavior of a function as \(x\) approaches infinity?

**Tip:** When dealing with limits, always check for open or closed points at specific \(x\)-values, as these often indicate whether a function is defined or not at that point!

Learn how to solve a function's limit as x approaches 4 and determine the value of f(4) from a graph. This problem covers key calculus concepts, including limits, discontinuities, and function behavior at specific points. Suitable for students in Grades 11-12.

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