**Graph Analysis: Piecewise-Defined Function**The graph displays a piecewise-defined function $ f $. It includes the following key characteristics:- The **y-axis** serves as a vertical asymptote.- The **domain** of $ f $ is $ (-\infty, -4) \cup (-4, 0) \cup (0, \infty) $.- The **range** of $ f $ is $ (-\infty, \infty) $.**Graph Description:**1. **First Segment (Left):** - Starts increasing from negative infinity, moving upwards towards $ x = -4 $. - The curve sharply dips towards $ x = 0 $ as it approaches $ y = 0 $.2. **Second Segment (Middle):** - Begins near $ x = -4 $ and breaks before $ x = 0 $. - Continuation on the right of the y-axis starts above $ x = 0 $.3. **Third Segment (Right):** - Starts above $ x = 0 $ and decreases outwards. - Continues to decrease as it moves towards positive infinity.**Point Details:**- Points plotted with closed or open dots denote integer coordinates and visible changes in the graph, indicating potential values and limits.**Task:**Answer parts $ a $ to $ j $ based on the graph characteristics. Use $ -\infty $ and $ \infty $ to denote unbounded decrease and increase, respectively. Write "DNE" if the quantity does not exist. **Given Problems:**a) $ f(-2) = $b) $ f(4) = $c) $ \lim_{x \to -7} f(x) = $d) $ \lim_{x \to -4} f(x) = $e) $ \lim_{x \to 0} f(x) = $f) $ \lim_{x \to 4} f(x) = $g) $ \lim_{x \to -2^+} f(x) = $h) $ \lim_{x \to -2^-} f(x) = $i) $ \lim_{x \to 9} f(x) = $j) \( \lim_{x \to

Answered: tv Pos) The graph is of a…

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

**Graph Analysis: Piecewise-Defined Function**

The graph displays a piecewise-defined function $ f $. It includes the following key characteristics:

- The **y-axis** serves as a vertical asymptote.
- The **domain** of $ f $ is $ (-\infty, -4) \cup (-4, 0) \cup (0, \infty) $.
- The **range** of $ f $ is $ (-\infty, \infty) $.

**Graph Description:**

1. **First Segment (Left):**
- Starts increasing from negative infinity, moving upwards towards $ x = -4 $.
- The curve sharply dips towards $ x = 0 $ as it approaches $ y = 0 $.

2. **Second Segment (Middle):**
- Begins near $ x = -4 $ and breaks before $ x = 0 $.
- Continuation on the right of the y-axis starts above $ x = 0 $.

3. **Third Segment (Right):**
- Starts above $ x = 0 $ and decreases outwards.
- Continues to decrease as it moves towards positive infinity.

**Point Details:**
- Points plotted with closed or open dots denote integer coordinates and visible changes in the graph, indicating potential values and limits.

**Task:**

Answer parts $ a $ to $ j $ based on the graph characteristics. Use $ -\infty $ and $ \infty $ to denote unbounded decrease and increase, respectively. Write "DNE" if the quantity does not exist.

**Given Problems:**

a) $ f(-2) = $

b) $ f(4) = $

c) $ \lim_{x \to -7} f(x) = $

d) $ \lim_{x \to -4} f(x) = $

e) $ \lim_{x \to 0} f(x) = $

f) $ \lim_{x \to 4} f(x) = $

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

h) $ \lim_{x \to -2^-} f(x) = $

i) $ \lim_{x \to 9} f(x) = $

j) \( \lim_{x \to

Expert Solution

Step 1

By observing graph we conclude on following points

a) at x=-2 , exact value of function is 2

f(-2)=2

b) at x=4 ,exact value of function is 1

f(4)=1

$\lim_{x \to - 7} f (x), y \to 5 \underset{x \to - 7}{l i m} f (x) = 5 d) \underset{x \to - 4}{l i m} f (x) = 2 e) a s x \to 0, f u n c t i o n c l o s e t o i n f i n i t y \underset{x \to 0}{l i m} f (x) = \infty f) a s x \to 4, f u n c t i o n c l o s e t o 2 t h e r e f o r e \underset{x \to - 7}{l i m} f (x) = 2 g) a s x \to r i g h t t o - 2, f u n c t i o n c l o s e t o 2 \underset{x \to - 2^{+}}{l i m} f (x) = 2 h) a s x \to l e f t t o - 2, f u n c t i o n c l o s e t o 0 \underset{x \to - 2^{-}}{l i m} f (x) = 0 i) a s x \to l e f t t o 9, f u n c t i o n c l o s e t o 0 \underset{x \to 9^{-}}{l i m} f (x) = 0 j) a s x \to i n f i n i t y, f u n c t i o n g o e s t o n e g a t i v e i n f i n i t y \underset{x \to \infty}{l i m} f (x) = - \infty$