Hi! I need these solved for this graph. A. f(-2)B. Lim f(x) X------>-2C. f(0)D. Lim f(x) X------>0E. f(2)F. Lim f(x) X------>2G. f(4)H. Lim f(x) X-------->4Graph:Also included these two other problems on this other image. Please answer them all so i can up vote your answer. Thanks everyone. Certainly! Below is the transcription and detailed explanation of the graph for an educational website.---### Understanding Graphical Representation of Functions#### Graph DescriptionThe graph displayed on this page represents a mathematical function depicted in the Cartesian coordinate system with the x-axis (horizontal) and y-axis (vertical).- The x-axis ranges from -2 to 5.- The y-axis ranges from -2 to 4.#### Key Features of the Graph1. **Axes and Scale**: - The x-axis is labeled with values from -2 to 5. - The y-axis is labeled with values from -2 to 4. - Both axes intersect at the origin (0,0).2. **Graph Behavior**: - There is a vertical asymptote at \( x = -2 \). - The function decreases towards negative infinity as it approaches \( x = -2 \) from the right. - At \( x = 0 \) and \( x = 2 \), there are open circles indicating discontinuities in the function. - The function value at \( x = 0 \) is approaching 2 from the left and right. - The function decreases to a minimum at \( x = 2 \) and then increases again, forming a valley shape. - At \( x = 4 \), the function has a closed circle hovering at \( y = 3.5 \).3. **General Shape**: - The graph shows peaks and valleys, indicating it is not a linear function. - The leftmost part of the graph starts at the top moving downwards steeply. - After the drop past \( x = -2 \), the graph increases steeply, moving through a valley. - Finally, there is a sharp increase with another steep incline starting from just before \( x = 5 \).4. **Discontinuities**: - There are distinct points of discontinuity at \( x = 0 \) and \( x = 2 \) where the function has open circles. - The value of the function at \( x = 4 \) extends with an open circle indicating a defined y-value for that x-coordinate.#### SummaryThis graph displays multiple characteristics such as asymptotes, discontinuities, and varying slopes. Understanding these elements helps in grasping the behavior of complex functions, particularly in evaluating limits and continuity. Evaluating such functions ### Calculus Problems: Limits and Continuity#### 1. Evaluate the limits of \( f(x) \) as \( x \) approaches 3 from the left, as \( x \) approaches 3, and as \( x \) approaches 3 from the right for the following function:Given:\[f(x) = \begin{cases} -x + 4 & \text{if } x < 3 \\x - 3 & \text{if } x \geq 3 \end{cases}\]**Tasks:**\[\lim_{x \to 3^-} f(x), \quad \lim_{x \to 3} f(x), \quad \lim_{x \to 3^+} f(x)\]---#### 2. (Task 2 is unspecified in the image and should be filled based on context or instructor's direction.)---#### 3. Determine whether the function is continuous at \( x = 5 \):Given:\[f(x) = \begin{cases} \frac{x^2 - 4x - 5}{x - 5} & \text{if } x < 5 \\x + 2 & \text{if } x \geq 5 \end{cases}\]**Tasks:**Check the continuity of \( f(x) \) at \( x = 5 \).

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Answered: 1. Evalaute lim ƒ(x), lim ƒ(x), lim…

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Calculus

1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ H-3- I-3 f(x) = { 2 -x+4 x - 3 x <3 I 23

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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Question

Hi! I need these solved for this graph. A. f(-2) B. Lim f(x) X------>-2 C. f(0) D. Lim f(x) X------>0 E. f(2) F. Lim f(x) X------>2 G. f(4) H. Lim f(x) X-------->4 Graph: Also included these two other problems on this other image. Please answer them all so i can up vote your answer. Thanks everyone.

Certainly! Below is the transcription and detailed explanation of the graph for an educational website.

---

### Understanding Graphical Representation of Functions

#### Graph Description
The graph displayed on this page represents a mathematical function depicted in the Cartesian coordinate system with the x-axis (horizontal) and y-axis (vertical).

- The x-axis ranges from -2 to 5.
- The y-axis ranges from -2 to 4.

#### Key Features of the Graph
1. **Axes and Scale**:
- The x-axis is labeled with values from -2 to 5.
- The y-axis is labeled with values from -2 to 4.
- Both axes intersect at the origin (0,0).

2. **Graph Behavior**:
- There is a vertical asymptote at \( x = -2 \).
- The function decreases towards negative infinity as it approaches \( x = -2 \) from the right.
- At \( x = 0 \) and \( x = 2 \), there are open circles indicating discontinuities in the function.
- The function value at \( x = 0 \) is approaching 2 from the left and right.
- The function decreases to a minimum at \( x = 2 \) and then increases again, forming a valley shape.
- At \( x = 4 \), the function has a closed circle hovering at \( y = 3.5 \).

3. **General Shape**:
- The graph shows peaks and valleys, indicating it is not a linear function.
- The leftmost part of the graph starts at the top moving downwards steeply.
- After the drop past \( x = -2 \), the graph increases steeply, moving through a valley.
- Finally, there is a sharp increase with another steep incline starting from just before \( x = 5 \).

4. **Discontinuities**:
- There are distinct points of discontinuity at \( x = 0 \) and \( x = 2 \) where the function has open circles.
- The value of the function at \( x = 4 \) extends with an open circle indicating a defined y-value for that x-coordinate.

#### Summary
This graph displays multiple characteristics such as asymptotes, discontinuities, and varying slopes. Understanding these elements helps in grasping the behavior of complex functions, particularly in evaluating limits and continuity. Evaluating such functions

### Calculus Problems: Limits and Continuity

#### 1. Evaluate the limits of \( f(x) \) as \( x \) approaches 3 from the left, as \( x \) approaches 3, and as \( x \) approaches 3 from the right for the following function:

Given:
\[
f(x) =
\begin{cases}
-x + 4 & \text{if } x < 3 \\
x - 3 & \text{if } x \geq 3
\end{cases}
\]

**Tasks:**
\[
\lim_{x \to 3^-} f(x), \quad \lim_{x \to 3} f(x), \quad \lim_{x \to 3^+} f(x)
\]

---

#### 2. (Task 2 is unspecified in the image and should be filled based on context or instructor's direction.)

---

#### 3. Determine whether the function is continuous at \( x = 5 \):

Given:
\[
f(x) =
\begin{cases}
\frac{x^2 - 4x - 5}{x - 5} & \text{if } x < 5 \\
x + 2 & \text{if } x \geq 5
\end{cases}
\]

**Tasks:**
Check the continuity of \( f(x) \) at \( x = 5 \).

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