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-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

-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

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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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. ---
Transcribed Image Text:--- **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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