Can you help me answer these 2 questions based on this graph. **Transcription for Educational Website:**A function $ f(x) $ is defined everywhere. The derivative graph, $ f'(x) $, is given below. Please answer questions 3-5 given this graph.**Graph Description:**The graph is a plot of $ y = f'(x) $ on a coordinate plane. The x-axis is labeled from 0 to 10 and the y-axis from -2 to 2.- The curve begins at the bottom left, approaching the point (0, -2).- It rises steadily to a local peak near (2, 2).- The curve slightly dips around (3, 1) before rising to another peak at (5, 2).- After descending to cross the x-axis at (7, 0), it reaches a trough at (8, -2).- Finally, it ascends sharply, exiting the graph at the upper right.This graph can be used to analyze the rate of change and critical points of the function $ f(x) $. The image contains a graph of a function $ f(x) $ and a multiple-choice question regarding where the function is decreasing. **Graph Explanation:**- The graph shows a curve plotted on a coordinate plane with the x-axis labeled at intervals of 2 units (0, 2, 4, 6).- The curve appears to decrease from the left of the origin and then increase at x = 0.- It seems to increase from somewhere around x = 1 to x = 3, decrease between x = 3 and x = 5, and increase again from x = 5 to x = 7.- The curve decreases again after x = 7.**Question:**Where is the function $ f(x) $ decreasing?**Options:**(a) $ (-\infty, 0) $(b) $ (2, 3) \cup (5, 7) $(c) $ (-\infty, 2) \cup (3, 5) \cup (7, \infty) $(d) $ (-\infty, 1) \cup (6, 8) $(e) $ (-\infty, 0) \cup (2, 3) \cup (6, 8) $

Name: Can you help me answer these 2 questions based on this graph. **Transc
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Description: Can you help me answer these 2 questions based on this graph. **Transcription for Educational Website:**A function $ f(x) $ is defined everywhere. The derivative graph, $ f'(x) $, is given below. Please answer questions 3-5 given this graph.**Gra

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Answered: A function f(x) is defined everywhere.…

Math

Calculus

A function f(x) is defined everywhere. The derivative graph, f'(x) is given below. Please answer questions 3-5 given th granh

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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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Can you help me answer these 2 questions based on this graph.

The image contains a graph of a function $ f(x) $ and a multiple-choice question regarding where the function is decreasing.

**Graph Explanation:**
- The graph shows a curve plotted on a coordinate plane with the x-axis labeled at intervals of 2 units (0, 2, 4, 6).
- The curve appears to decrease from the left of the origin and then increase at x = 0.
- It seems to increase from somewhere around x = 1 to x = 3, decrease between x = 3 and x = 5, and increase again from x = 5 to x = 7.
- The curve decreases again after x = 7.

**Question:**
Where is the function $ f(x) $ decreasing?

**Options:**
(a) $ (-\infty, 0) $

(b) $ (2, 3) \cup (5, 7) $

(c) $ (-\infty, 2) \cup (3, 5) \cup (7, \infty) $

(d) $ (-\infty, 1) \cup (6, 8) $

(e) $ (-\infty, 0) \cup (2, 3) \cup (6, 8) $

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