https://file.aiquickdraw.com/mathbot/file/1726488198459k5e0ugef.jpg

Let's evaluate the two questions based on the graph shown in the image:

### a) \( f(-2) \)
We are asked to find the value of the function at \( x = -2 \). Looking at the graph at \( x = -2 \), there is an open circle on the curve at \( y = 4 \), which indicates that the function is not defined there. However, there is a solid point at \( y = -2 \), which represents the actual value of the function at this point.

So, 
\[
f(-2) = -2
\]

### b) \( \lim_{x \to 2} f(x) \)
We are asked to find the limit of the function as \( x \) approaches 2. From the graph, as \( x \) approaches 2 from both the left and the right, the function approaches \( y = 3 \). There is an open circle at \( x = 2 \), indicating that the function is not defined at this point, but the limit depends on the behavior around it, not at the point itself.

So, 
\[
\lim_{x \to 2} f(x) = 3
\]

Would you like any further details on these concepts?

Here are 5 related questions for practice:
1. What is \( \lim_{x \to -2} f(x) \)?
2. What is \( f(4) \) based on the graph?
3. What does it mean when a graph has an open circle at a point?
4. How do you determine limits graphically?
5. What is the difference between a limit and the actual function value at a point?

**Tip**: When finding limits graphically, always check the values the function approaches from both sides of the point in question.

Use the graph of the function to evaluate f(-2) and the limit as x approaches 2 of f(x).

Learn how to evaluate the function at x = -2 and find the limit as x approaches 2 from the graph. The solution involves concepts of function evaluation and the limit theorem, useful for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation