---**32. The graph of a function \( g(x) \) is shown below:**![Graph of function \( g(x) \)](graph_url)This graph shows the function \( g(x) \) plotted on the coordinate plane. The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10. The graph of \( g(x) \) forms a piecewise shape with distinct linear segments connecting the points at:- (-10, 0)- (-4, 0)- (0, 6)- (6, 6)- (10, 0)**Question:** **On what interval of \( x \)-values is the function \( g(x) \) increasing?****Options:**- **A. (-3, 6)**- **B. (0, 3)**- **C. (1, 10)**- **D. (6, 10)**The function \( g(x) \) is increasing on the interval where the graph is rising as \( x \) increases. From the graph, identify the segments where the slope is positive to determine the correct answer.**Explanation of the Graph:**The graph starts flat at \( y = 0 \) from \( x = -10 \) to \( x = -4 \), indicating that the function \( g(x) \) remains constant in this interval. Then, the graph rises from \( x = -4 \) to \( x = 0 \), increasing from \( y = 0 \) to \( y = 6 \). Next, the function stays flat at \( y = 6 \) from \( x = 0 \) to \( x = 6 \). Lastly, the graph decreases from \( x = 6 \) to \( x = 10 \), dropping back to \( y = 0 \).Therefore, the function \( g(x) \) is increasing on the interval \([-4, 0]\).**Powered by LinkIt!**Note: The options provided in the original question do not align with the interval where the function \( g(x) \) is actually increasing. Ensure to cross-verify the options with the graph for clarity.---

from graph g(0)=-3 g(1)=0 g(2)=5 g(3)=6 g(4)=6 g(5)=6 g(6)=6 g(7)=4.5 g(8)=3 g(10)=0

Answered: -2 6 -10 -8 -6 -4 6 8 -8 -10 On what…

-2 6 -10 -8 -6 -4 6 8 -8 -10 On what interval of x-values is the function g(x) increasing? A. (-3, 6) B. (0, 3) C. (1, 10) D. (6, 10) -6 4 2 0 -2 -4 2 4 10

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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Question

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**32. The graph of a function \( g(x) \) is shown below:**

![Graph of function \( g(x) \)](graph_url)

This graph shows the function \( g(x) \) plotted on the coordinate plane. The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10. The graph of \( g(x) \) forms a piecewise shape with distinct linear segments connecting the points at:

- (-10, 0)
- (-4, 0)
- (0, 6)
- (6, 6)
- (10, 0)

**Question:**
**On what interval of \( x \)-values is the function \( g(x) \) increasing?**

**Options:**
- **A. (-3, 6)**
- **B. (0, 3)**
- **C. (1, 10)**
- **D. (6, 10)**

The function \( g(x) \) is increasing on the interval where the graph is rising as \( x \) increases. From the graph, identify the segments where the slope is positive to determine the correct answer.

**Explanation of the Graph:**
The graph starts flat at \( y = 0 \) from \( x = -10 \) to \( x = -4 \), indicating that the function \( g(x) \) remains constant in this interval. Then, the graph rises from \( x = -4 \) to \( x = 0 \), increasing from \( y = 0 \) to \( y = 6 \). Next, the function stays flat at \( y = 6 \) from \( x = 0 \) to \( x = 6 \). Lastly, the graph decreases from \( x = 6 \) to \( x = 10 \), dropping back to \( y = 0 \).

Therefore, the function \( g(x) \) is increasing on the interval \([-4, 0]\).

**Powered by LinkIt!**

Note: The options provided in the original question do not align with the interval where the function \( g(x) \) is actually increasing. Ensure to cross-verify the options with the graph for clarity.

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