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.

Answered: The function f graphed below is defined…

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.

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