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4 4 2 2 -4 -2 2 4 -4 -2 4 -2 -2 -4 -4

4 4 2 2 -4 -2 2 4 -4 -2 4 -2 -2 -4 -4

Calculus: Early Transcendentals
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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For the given graph of the function f, on the left, sketch the graph of of f′ on the right.

The image contains two separate graphs, each plotted on its own set of Cartesian axes. ### Details of Each Graph: #### Left Graph: - **Type of Graph:** This is a plot of a rational function, likely resembling the form \( f(x) = \frac{1}{x^2} \). - **Characteristics:** - The graph exhibits a vertical asymptote at \( x = 0 \), where the function is undefined. As the graph approaches this line from either side, the values of the function tend towards infinity. - The curve is situated in the first and second quadrants. - As \( x \) moves away from zero in either direction, the values of the function decrease towards zero. - **Symmetry:** The graph is symmetric with respect to the y-axis, indicating it's an even function. #### Right Graph: - **Type of Graph:** This graph is a horizontal line at \( y = 0 \). - **Characteristics:** - It represents a constant function with all y-values equal to zero, irrespective of the x-values. - The line runs along the x-axis from negative to positive infinity. ### General Observations: - Both graphs share the same axes specifications: - **X-Axis:** Ranges roughly from -4 to 4. - **Y-Axis:** Ranges from -4 to 4. - **Axes Intersection:** Both x and y axes intersect at the origin point (0, 0). This visualization provided here aims to explain the basic properties and behavior of a rational function with a vertical asymptote alongside a simple constant function as a basis for comparison.
Transcribed Image Text:The image contains two separate graphs, each plotted on its own set of Cartesian axes. ### Details of Each Graph: #### Left Graph: - **Type of Graph:** This is a plot of a rational function, likely resembling the form \( f(x) = \frac{1}{x^2} \). - **Characteristics:** - The graph exhibits a vertical asymptote at \( x = 0 \), where the function is undefined. As the graph approaches this line from either side, the values of the function tend towards infinity. - The curve is situated in the first and second quadrants. - As \( x \) moves away from zero in either direction, the values of the function decrease towards zero. - **Symmetry:** The graph is symmetric with respect to the y-axis, indicating it's an even function. #### Right Graph: - **Type of Graph:** This graph is a horizontal line at \( y = 0 \). - **Characteristics:** - It represents a constant function with all y-values equal to zero, irrespective of the x-values. - The line runs along the x-axis from negative to positive infinity. ### General Observations: - Both graphs share the same axes specifications: - **X-Axis:** Ranges roughly from -4 to 4. - **Y-Axis:** Ranges from -4 to 4. - **Axes Intersection:** Both x and y axes intersect at the origin point (0, 0). This visualization provided here aims to explain the basic properties and behavior of a rational function with a vertical asymptote alongside a simple constant function as a basis for comparison.
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