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Withe the red graph being f(x) and the blue graph being g(x), what is lim*x*→2^− [*f*(*x*)+*g*(*x*)]

To evaluate  

\[
\lim_{x \to 2^-} [f(x) + g(x)]
\]

we analyze the left-hand limit (\(x \to 2^-\)) of both functions \(f(x)\) (red) and \(g(x)\) (blue).  

### Step 1: Identify \(\lim_{x \to 2^-} f(x)\)
From the red graph, as \(x\) approaches \(2\) from the left, the function value approaches approximately **-1**.

### Step 2: Identify \(\lim_{x \to 2^-} g(x)\)
From the blue graph, as \(x\) approaches \(2\) from the left, the function value approaches approximately **-1**.

### Step 3: Compute the Sum
\[
\lim_{x \to 2^-} [f(x) + g(x)] = (-1) + (-1) = -2
\]

Thus, the left-hand limit is:

\[
\lim_{x \to 2^-} [f(x) + g(x)] = -2
\]

Would you like further clarification or details on this?  

### Related Questions:
1. What is \(\lim_{x \to 2^+} [f(x) + g(x)]\)?
2. Are there any discontinuities in \(f(x) + g(x)\) at \(x = 2\)?
3. How would you describe the behavior of \(f(x)\) and \(g(x)\) separately at \(x=2\)?
4. What does the sum of two discontinuous functions tell us about their combined behavior?
5. Can we conclude that \(f(x) + g(x)\) is continuous at \(x=2\)?

### Tip:
When computing limits graphically, always check for open and closed circles at the approach points to determine left-hand and right-hand behavior.

With the red graph being f(x) and the blue graph being g(x), what is lim*x*→2^- [f(x)+g(x)]?

Explore the left-hand limit of the sum f(x) + g(x) as x approaches 2 using graphical analysis. This problem uses the limit addition theorem and involves identifying values from graphical representations of f(x) and g(x). Suitable for Grades 11-12 students.

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