was wondering what the answers to a-f were so that I can check my answers! **Problem 3: Analysis of the Function \( f(x) \)**Given the function \( f(x) \) whose graph is displayed, answer the following questions. The graph illustrates a range of behavior for \( f(x) \) around \( x = 0 \) and extends towards both positive and negative infinity.### Graph Details:- The graph shows a discontinuity at \( x = 0 \), with an open circle indicating a hole at this point on the curve that approaches the vertical axis from both sides.- For \( x < 0 \), the curve is drawn downwards and seems to approach a horizontal asymptote.- For \( x > 0 \), the curve goes upward beyond the vertical axis and approaches another horizontal asymptote.- A horizontal asymptote is shown as a dashed line on both sides for \( x \to -\infty \) and \( x \to +\infty \).### Questions:(a) \( \lim_{{x \to 0}} f(x) = \) (b) \( \lim_{{x \to 0^+}} f(x) = \)(c) \( f(0) = \)(d) \( \lim_{{x \to \infty}} f(x) = \)(e) For what points is \( f \) not continuous?(f) For what points does \( \frac{d}{dx} \) not exist?### Observations:- The graph indicates a discontinuity at \( x = 0 \), suggesting that \( f(x) \) is not continuous there.- The function's limits as \( x \to 0 \), \( x \to 0^+ \), and \( x \to \infty \) should be evaluated based on behavior approaching these points.- Derivatives might not exist at points where the function is not continuous or where the graph has sharp corners or cusps.

Answered: Image /qna-images/answer/f6222f5b-463a-4300-b9cc-aa236f94e5f2.jpg

Answered: 3. Let f(r) be the function whose graph…

3. Let f(r) be the function whose graph appears below. (b) lim f(r) = I >0+ (c) f(0) = (d) lim f(r) = (e) For what points is f not continuous? (a) lim f(r) = (f) For what points does 4 not exist? %3D

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

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was wondering what the answers to a-f were so that I can check my answers!

**Problem 3: Analysis of the Function \( f(x) \)**

Given the function \( f(x) \) whose graph is displayed, answer the following questions. The graph illustrates a range of behavior for \( f(x) \) around \( x = 0 \) and extends towards both positive and negative infinity.

### Graph Details:
- The graph shows a discontinuity at \( x = 0 \), with an open circle indicating a hole at this point on the curve that approaches the vertical axis from both sides.
- For \( x < 0 \), the curve is drawn downwards and seems to approach a horizontal asymptote.
- For \( x > 0 \), the curve goes upward beyond the vertical axis and approaches another horizontal asymptote.
- A horizontal asymptote is shown as a dashed line on both sides for \( x \to -\infty \) and \( x \to +\infty \).

### Questions:

(a) \( \lim_{{x \to 0}} f(x) = \)

(b) \( \lim_{{x \to 0^+}} f(x) = \)

(c) \( f(0) = \)

(d) \( \lim_{{x \to \infty}} f(x) = \)

(e) For what points is \( f \) not continuous?

(f) For what points does \( \frac{d}{dx} \) not exist?

### Observations:
- The graph indicates a discontinuity at \( x = 0 \), suggesting that \( f(x) \) is not continuous there.
- The function's limits as \( x \to 0 \), \( x \to 0^+ \), and \( x \to \infty \) should be evaluated based on behavior approaching these points.
- Derivatives might not exist at points where the function is not continuous or where the graph has sharp corners or cusps.

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