https://file.aiquickdraw.com/mathbot/file/1729439949856il1ja0e3.jpg

I see that you've uploaded an image containing several questions based on a graph. Let me extract the details and work through the parts one by one.

### Part 1: 
The question is asking about the limit of \( f(x) \) as \( x \) approaches \( -1 \) from the left-hand side (denoted as \( x \to -1^- \)).

From the graph, as \( x \) approaches \( -1 \) from the left, the function \( f(x) \) decreases without bound. Hence:
\[
\lim_{x \to -1^-} f(x) = -\infty
\]

### Part 2:
This part is asking about the limit as \( x \to -1^+ \) (approaching from the right side).

From the graph, as \( x \) approaches \( -1 \) from the right, the function increases without bound. Therefore:
\[
\lim_{x \to -1^+} f(x) = \infty
\]

### Part 3:
Here, it asks for the limit of \( f(x) \) as \( x \) approaches infinity, \( \lim_{x \to \infty} f(x) \).

From the graph, as \( x \) goes to infinity, it looks like \( f(x) \) approaches the horizontal asymptote at \( y = 0 \). So:
\[
\lim_{x \to \infty} f(x) = 0
\]

### Part 4:
This part asks for the limit as \( x \to -\infty \).

From the graph, as \( x \) goes to negative infinity, \( f(x) \) again approaches the horizontal asymptote at \( y = 0 \). Thus:
\[
\lim_{x \to -\infty} f(x) = 0
\]

### Part 5:
This part asks if the graph is increasing over at least one interval and if it is decreasing over at least one interval.

From the graph:
- The function is **increasing** on the interval \( (-1, \infty) \).
- The function is **decreasing** on the interval \( (-\infty, -1) \).

So the answer to both questions is **True**.

### Part 6:
This part asks for the interval over which the graph is increasing. From the graph, the function is increasing for:
\[
(-1, \infty)
\]

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Would you like a further breakdown of any specific part or the next steps? 

Here are 5 related questions for practice:
1. What happens to \( f(x) \) as \( x \to 0^+ \)?
2. Identify the vertical asymptote(s) for the graph.
3. What would be the domain of the function \( f(x) \)?
4. Does the function ever cross the horizontal asymptote? Why or why not?
5. What is the range of the function based on the graph?

### Tip:
When analyzing graphs for limits, always carefully examine behavior near key points (like where asymptotes occur) and at extreme values (as \( x \to \infty \) or \( x \to -\infty \)).

The problem is related to analyzing limits and behavior of a function based on its graph. The user needs to determine specific limits as x approaches certain values, identify intervals of increase and decrease, and describe the function's behavior near asymptotes.

This problem involves analyzing the graph of a function to determine its limits at key points, identify intervals where the function is increasing or decreasing, and describe the function's behavior near asymptotes. This problem is suitable for students in Grade 11-12 or Calculus 1.

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