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The function f graphed below is defined by a polynomial expression of degree 4. Use the graph to solve the exercise.   (a) If f is increasing on an interval, then the y-values of the points on the graph  ---Select--- fall rise as the x-values increase. From the graph of f we see that f is increasing on the intervals (b) If f is decreasing on an interval, then the y-values of the points on the graph  ---Select--- fall rise as the x-values increase. From the graph of f shown above, we see that f is decreasing on the intervals

The function f graphed below is defined by a polynomial expression of degree 4. Use the graph to solve the exercise.   (a) If f is increasing on an interval, then the y-values of the points on the graph  ---Select--- fall rise as the x-values increase. From the graph of f we see that f is increasing on the intervals (b) If f is decreasing on an interval, then the y-values of the points on the graph  ---Select--- fall rise as the x-values increase. From the graph of f shown above, we see that f is decreasing on the intervals

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The function f graphed below is defined by a polynomial expression of degree 4. Use the graph to solve the exercise.

 
(a) If f is increasing on an interval, then the y-values of the points on the graph  ---Select--- fall rise as the x-values increase. From the graph of f we see that f is increasing on the intervals
(b) If f is decreasing on an interval, then the y-values of the points on the graph  ---Select--- fall rise as the x-values increase. From the graph of f shown above, we see that f is decreasing on the intervals
### Graph of a Function \( f \) #### Description: The graph above depicts a function \( f \) plotted on a Cartesian coordinate system. This function exhibits varying behaviors across different intervals of the \( x \)-axis. #### Axes: - The \( x \)-axis and \( y \)-axis are both labeled. The \( x \)-axis runs horizontally, while the \( y \)-axis runs vertically. - Both axes are marked with evenly spaced grid lines, indicating units along each axis. - The origin of the graph is at the intersection of the \( x \)-axis and \( y \)-axis, with coordinates (0,0). #### Plot Details: - The function \( f \) is represented by a red curve. - The curve starts from a point below \( x = 0 \) on the \( y \)-axis. - The curve ascends, reaching a local maximum above \( y = 3 \) at approximately \( x = 1 \). - The curve then descends to a local minimum slightly above \( y = 1 \) at approximately \( x = 3 \). - Afterward, the curve rises again to another local maximum around \( y = 3 \) at approximately \( x = 5 \) and descends thereafter. #### Key Observations: - **Local Maximum**: The graph has noticeable peaks above the \( x \)-axis, indicating local maximum points where the function's rate of change switches from positive to negative. - **Local Minimum**: There is a trough between the peaks indicating a local minimum point where the function's rate of change switches from negative to positive. This graph can serve as a practical example for a variety of mathematical concepts, including finding local extrema (maxima and minima), analyzing the behavior of polynomial functions, and understanding the nature of continuous functions.
Transcribed Image Text:### Graph of a Function \( f \) #### Description: The graph above depicts a function \( f \) plotted on a Cartesian coordinate system. This function exhibits varying behaviors across different intervals of the \( x \)-axis. #### Axes: - The \( x \)-axis and \( y \)-axis are both labeled. The \( x \)-axis runs horizontally, while the \( y \)-axis runs vertically. - Both axes are marked with evenly spaced grid lines, indicating units along each axis. - The origin of the graph is at the intersection of the \( x \)-axis and \( y \)-axis, with coordinates (0,0). #### Plot Details: - The function \( f \) is represented by a red curve. - The curve starts from a point below \( x = 0 \) on the \( y \)-axis. - The curve ascends, reaching a local maximum above \( y = 3 \) at approximately \( x = 1 \). - The curve then descends to a local minimum slightly above \( y = 1 \) at approximately \( x = 3 \). - Afterward, the curve rises again to another local maximum around \( y = 3 \) at approximately \( x = 5 \) and descends thereafter. #### Key Observations: - **Local Maximum**: The graph has noticeable peaks above the \( x \)-axis, indicating local maximum points where the function's rate of change switches from positive to negative. - **Local Minimum**: There is a trough between the peaks indicating a local minimum point where the function's rate of change switches from negative to positive. This graph can serve as a practical example for a variety of mathematical concepts, including finding local extrema (maxima and minima), analyzing the behavior of polynomial functions, and understanding the nature of continuous functions.
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