Use the graph to find the indicated limits.

Step 1 of 3 :  Find limx→−2−f(x).
x
−10
−5
5
10
y
−10
−5
5
10
Cartesian Coordinate PlaneThe horizontal axis is labeled with x. The horizontal axis contains 21 grid lines, starts at -10, and ends at 10; and the axis is labeled with the values: -10, -5, 5, 10.The vertical axis is labeled with y. The vertical axis contains 21 grid lines, starts at -10, and ends at 10; and the axis is labeled with the values: -10, -5, 5, 10.Piecewise GraphThe graph is made up of a set of different curves, defined over the 2 regions,for the curves: Left Curve and Right Curve.Region 1The region of the coordinate plane containing horizontal values to the left of the value 2 units left of the origin and all vertical values.Left CurveA solid curve is drawn with the equation f(x)=−2x+2−1.Vertical AsymptoteA dashed vertical line segment is drawn 2 units left of the vertical axis.Region 2The region of the coordinate plane containing horizontal values to the right of the value 2 units left of the origin and all vertical values.Right CurveA solid curve is drawn with the equation f(x)=2x+2−2.Vertical AsymptoteA dashed vertical line segment is drawn 2 units left of the vertical axis.

To find the limit \(\lim_{{x \to -2^-}} f(x)\), we need to analyze the behavior of the function as \(x\) approaches \(-2\) from the left side, denoted by the superscript \(^-\). Based on your description of the graph and the equations of the curves, we can follow these steps:

### Step 1: Identify the equation of the curve to the left of \(x = -2\).
The graph in Region 1, which is the left region, corresponds to the function \(f(x) = -2x + 2 - 1\). This equation defines the behavior of the function as \(x\) approaches \(-2\) from the left side.

### Step 2: Evaluate the limit as \(x\) approaches \(-2\) from the left.
We will substitute \(x = -2\) into the equation \(f(x) = -2x + 2 - 1\):

\[
f(x) = -2(-2) + 2 - 1 = 4 + 2 - 1 = 5
\]

### Conclusion:
As \(x\) approaches \(-2\) from the left (\(x \to -2^-\)), the value of \(f(x)\) approaches \(5\).

Thus, \(\lim_{{x \to -2^-}} f(x) = 5\).

Would you like details on how to find other types of limits or clarify this one?

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Here are 5 related questions for further practice:

1. What is \(\lim_{{x \to -2^+}} f(x)\) from the graph?
2. What is \(\lim_{{x \to 2}} f(x)\) if there is a vertical asymptote?
3. How do we find \(\lim_{{x \to 0}} f(x)\) if the function is continuous at \(x = 0\)?
4. How does the behavior of a graph near a vertical asymptote affect limits?
5. What is the difference between one-sided and two-sided limits?

**Tip:** Always pay attention to whether you are approaching a point from the left (\(^-\)) or from the right (\(^+\)) when finding one-sided limits.

Use the graph to find the indicated limits. Step 1 of 3: Find limx→−2−f(x).

Explore how to find the limit of a piecewise function as x approaches -2 from the left. This problem focuses on key calculus concepts like limits, one-sided limits, and behavior near vertical asymptotes. Suitable for high school students in Grades 11-12.

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