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The diagram shows the graph of a sinusoidal curve, drawn in radian mode. a.) Write an equation for this graph. b.) find the three smallest positive x-intercepts, rounding your answers to three decimal places. Show your reasoning that led you to your answers. c.) write an expression(s) for all of the x-intercepts.

The diagram shows the graph of a sinusoidal curve, drawn in radian mode. a.) Write an equation for this graph. b.) find the three smallest positive x-intercepts, rounding your answers to three decimal places. Show your reasoning that led you to your answers. c.) write an expression(s) for all of the x-intercepts.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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The diagram shows the graph of a sinusoidal curve, drawn in radian mode.

a.) Write an equation for this graph.

b.) find the three smallest positive x-intercepts, rounding your answers to three decimal places. Show your reasoning that led you to your answers.

c.) write an expression(s) for all of the x-intercepts. 

### Explanation of the Graph This graph depicts a function that oscillates in a wave-like pattern, specifically a trigonometric or periodic function. The x-axis represents the horizontal scale, while the y-axis represents the vertical scale. #### Key Features: 1. **Peak Points**: - The graph reaches its peak values (maximum points) at approximately (1.5, 10), and (6, 10). 2. **Valley Points**: - The graph reaches its lowest values (minimum points) at approximately (4, -5), and (9, -5). 3. **Intercepts**: - The graph intersects the x-axis at approximately (0, -1), indicating an important point. - Another marked intercept is at (3π/4, -4), illustrated with a black dot. 4. **Periodic Nature**: - The pattern repeats itself after a fixed interval, which suggests that the function is periodic. #### Detailed Description: - **Amplitude**: The graph oscillates between approximately 10 and -5. This indicates the range of y-values the function takes. - **Marked Points**: - The point (0, -1) is an intercept on the x-axis. - The point (3π/4, -4) is explicitly marked on the graph, signifying its importance in the function being illustrated. - **Grid Lines**: The background has grid lines to help determine coordinates accurately, enhancing readability and accuracy. ### Conclusion This graph is an excellent example for studying wave functions, trigonometric function behavior, and periodicity in mathematical education. The coordinates and markings help in understanding specific points of interest in the function, like intercepts, maximum, and minimum points.
Transcribed Image Text:### Explanation of the Graph This graph depicts a function that oscillates in a wave-like pattern, specifically a trigonometric or periodic function. The x-axis represents the horizontal scale, while the y-axis represents the vertical scale. #### Key Features: 1. **Peak Points**: - The graph reaches its peak values (maximum points) at approximately (1.5, 10), and (6, 10). 2. **Valley Points**: - The graph reaches its lowest values (minimum points) at approximately (4, -5), and (9, -5). 3. **Intercepts**: - The graph intersects the x-axis at approximately (0, -1), indicating an important point. - Another marked intercept is at (3π/4, -4), illustrated with a black dot. 4. **Periodic Nature**: - The pattern repeats itself after a fixed interval, which suggests that the function is periodic. #### Detailed Description: - **Amplitude**: The graph oscillates between approximately 10 and -5. This indicates the range of y-values the function takes. - **Marked Points**: - The point (0, -1) is an intercept on the x-axis. - The point (3π/4, -4) is explicitly marked on the graph, signifying its importance in the function being illustrated. - **Grid Lines**: The background has grid lines to help determine coordinates accurately, enhancing readability and accuracy. ### Conclusion This graph is an excellent example for studying wave functions, trigonometric function behavior, and periodicity in mathematical education. The coordinates and markings help in understanding specific points of interest in the function, like intercepts, maximum, and minimum points.
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