10- 8- 6- 4- 2- Match the graph of f with the correct sign chart. -8 -6 -4 -2-2- -4- -6- -8- -10 Now, use all of the gathered information to choose the correct sign chart below. O A. f(x) В. f(x) - - ND 0 + + X -3 -3 O C. f(x) + O D. f(x) + ND + X -3 -3

Calculus: Early Transcendentals
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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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### Graph Analysis and Sign Chart Matching

In this exercise, you are tasked with matching the graph of the function \( f \) with the correct sign chart for its derivative \( f'(x) \).

#### Graph Description:
The graph shown is a curve plotted on a Cartesian coordinate system. The y-axis is labeled and ranges from -10 to 10 in increments of 2. The x-axis is labeled, ranging from -10 to 2 in increments of 2 as well. The curve appears to have a vertical asymptote near \( x = -3 \), and it is decreasing throughout the visible portion of the graph.

#### Sign Chart Options:
You have four different sign charts to choose from, labeled A, B, C, and D. Each sign chart describes the behavior of the derivative \( f'(x) \) with respect to \( x \) near \( x = -3 \).

- **Option A**: 
  - \( f'(x) \): \(- - - \text{ ND } - - -\)
  - A non-defined point at \( x = -3 \).

- **Option B**: 
  - \( f'(x) \): \(+ + + \, 0 \, + + +\)
  - A zero at \( x = -3 \).

- **Option C**: 
  - \( f'(x) \): \(+ + + \text{ ND } + + +\)
  - A non-defined point at \( x = -3 \).

- **Option D**: 
  - \( f'(x) \): \(- - - \, 0 \, - - -\)
  - A zero at \( x = -3 \).

Your task is to analyze the graph and choose the corresponding sign chart based on the behavior of the function and its derivative around the critical point \( x = -3 \). Consider if the function is increasing or decreasing, and whether the derivative might be undefined or zero at this point.
Transcribed Image Text:### Graph Analysis and Sign Chart Matching In this exercise, you are tasked with matching the graph of the function \( f \) with the correct sign chart for its derivative \( f'(x) \). #### Graph Description: The graph shown is a curve plotted on a Cartesian coordinate system. The y-axis is labeled and ranges from -10 to 10 in increments of 2. The x-axis is labeled, ranging from -10 to 2 in increments of 2 as well. The curve appears to have a vertical asymptote near \( x = -3 \), and it is decreasing throughout the visible portion of the graph. #### Sign Chart Options: You have four different sign charts to choose from, labeled A, B, C, and D. Each sign chart describes the behavior of the derivative \( f'(x) \) with respect to \( x \) near \( x = -3 \). - **Option A**: - \( f'(x) \): \(- - - \text{ ND } - - -\) - A non-defined point at \( x = -3 \). - **Option B**: - \( f'(x) \): \(+ + + \, 0 \, + + +\) - A zero at \( x = -3 \). - **Option C**: - \( f'(x) \): \(+ + + \text{ ND } + + +\) - A non-defined point at \( x = -3 \). - **Option D**: - \( f'(x) \): \(- - - \, 0 \, - - -\) - A zero at \( x = -3 \). Your task is to analyze the graph and choose the corresponding sign chart based on the behavior of the function and its derivative around the critical point \( x = -3 \). Consider if the function is increasing or decreasing, and whether the derivative might be undefined or zero at this point.
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