**Instructional Text:**Use the graph below to find the limits.**Graph Description:**The graph provided is labeled $ y = f(x) $ and is plotted on a Cartesian coordinate system with the x-axis ranging approximately from -6 to 6 and the y-axis from -4 to 4.**Detailed Explanation of the Graph:**1. **Linear Segment:** - The graph shows a downward-sloping linear segment on the left, starting from $x = -6$ and extending to just before $x = -2$. - This line crosses the y-axis at approximately $ y = 4 $ and continues down to $ y = 0 $ at $ x = -2 $, where there is an open circle, indicating the value is not included at that point.2. **Curve:** - From $x = -2$, the graph curves downwards in a parabolic shape and reaches a minimum at approximately $ x = 2 $. - The curve continues smoothly from $ y = 0 $ at $ x = -2 $, dips to $ y = -4 $ at its lowest point, and rises back up to $ y = -2 $ at $ x = 4 $.3. **Discontinuity:** - At $ x = 4 $, there is a solid dot at $ y = 3 $, indicating a defined value of $ f(x) = 3 $ at this point. - There is also an open circle at $ y = -2 $ at $ x = 4 $, suggesting the function approaches this value but doesn’t include it at exactly $ x = 4 $.4. **Horizontal Arrow:** - Beyond $ x = 4 $, the graph indicates an arrow pointing horizontally to the right, suggesting the function continues indefinitely in this direction.**Usage Context:**Use this graph to analyze limits, particularly focusing on points of discontinuity and evaluating the behavior of the function as it approaches specific x-values. **Limits Exercise**1. Evaluate the limit: \[ 1. \quad \lim_{{x \to 0^-}} f(x) = \text{(Your answer)} \]2. Evaluate the limit from the right: \[ 2. \quad \lim_{{x \to 0^+}} f(x) = \text{(Your answer)} \]**Instructions:**- Enter your answers in the spaces provided.- Consider the behavior of the function $ f(x) $ as $ x $ approaches 0 from both the left ($0^-$) and the right ($0^+$).

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Description: **Instructional Text:**Use the graph below to find the limits.**Graph Description:**The graph provided is labeled $ y = f(x) $ and is plotted on a Cartesian coordinate system with the x-axis ranging approximately from -6 to 6 and the y-axis from -

Answered: 1. lim f(x) = X→0¬ Your answer 2. lim…

Math

Calculus

1. lim f(x) = X→0¬ Your answer 2. lim f(x) = x→0+ %3D 2.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Topic Video

Question

**Instructional Text:**

Use the graph below to find the limits.

**Graph Description:**

The graph provided is labeled $ y = f(x) $ and is plotted on a Cartesian coordinate system with the x-axis ranging approximately from -6 to 6 and the y-axis from -4 to 4.

**Detailed Explanation of the Graph:**

1. **Linear Segment:**
- The graph shows a downward-sloping linear segment on the left, starting from $x = -6$ and extending to just before $x = -2$.
- This line crosses the y-axis at approximately $ y = 4 $ and continues down to $ y = 0 $ at $ x = -2 $, where there is an open circle, indicating the value is not included at that point.

2. **Curve:**
- From $x = -2$, the graph curves downwards in a parabolic shape and reaches a minimum at approximately $ x = 2 $.
- The curve continues smoothly from $ y = 0 $ at $ x = -2 $, dips to $ y = -4 $ at its lowest point, and rises back up to $ y = -2 $ at $ x = 4 $.

3. **Discontinuity:**
- At $ x = 4 $, there is a solid dot at $ y = 3 $, indicating a defined value of $ f(x) = 3 $ at this point.
- There is also an open circle at $ y = -2 $ at $ x = 4 $, suggesting the function approaches this value but doesn’t include it at exactly $ x = 4 $.

4. **Horizontal Arrow:**
- Beyond $ x = 4 $, the graph indicates an arrow pointing horizontally to the right, suggesting the function continues indefinitely in this direction.

**Usage Context:**

Use this graph to analyze limits, particularly focusing on points of discontinuity and evaluating the behavior of the function as it approaches specific x-values.

**Limits Exercise**

1. Evaluate the limit:

\[
1. \quad \lim_{{x \to 0^-}} f(x) = \text{(Your answer)}
\]

2. Evaluate the limit from the right:

\[
2. \quad \lim_{{x \to 0^+}} f(x) = \text{(Your answer)}
\]

**Instructions:**
- Enter your answers in the spaces provided.
- Consider the behavior of the function $ f(x) $ as $ x $ approaches 0 from both the left ($0^-$) and the right ($0^+$).

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