Anonymous
Nov 14
Plot the following graphs in the same axis; y=2^x, y=3^x and y=4^x?
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ChatGPT
Nov 14
To plot the graphs of y=2^x, y=3^x, and y=4^x in the same axis, we can use a graphing calculator or software like Desmos. Here is the graph:
The graph shows that y=2^x is the lowest curve, y=3^x is in the middle, and y=4^x is the highest curve. As x increases, the curves grow exponentially, with y=4^x growing the fastest.
The graph shows that y=2^x is the lowest curve, y=3^x is in the middle, and y=4^x is the highest curve. As x increases, the curves grow exponentially, with y=4^x growing the fastest.
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Google Gemini AI
Nov 14
To plot the graphs of y = 2^x, y = 3^x, and y = 4^x on the same axis, follow these steps:
1. Create a coordinate plane by drawing two perpendicular lines, one for the x-axis and one for the y-axis. Label the x-axis with "x" and the y-axis with "y".
2. Choose appropriate scales for the x- and y-axes. Since the graphs are exponential functions, it is recommended to use logarithmic scales to better visualize the differences in growth rates.
3. Plot the points for each function.
- For y = 2^x, calculate a few values of y for different values of x, such as (0, 1), (1, 2), (2, 4), and (3, 8). Plot these points on the graph.
- Repeat the process for y = 3^x and y = 4^x, calculating points such as (1, 3), (2, 9), and (3, 27) for y = 3^x, and (1, 4), (2, 16), and (3, 64) for y = 4^x.
4. Connect the points for each function with a smooth curve. The curve for y = 2^x will have a steep slope, while the curves for y = 3^x and y = 4^x will have less steep slopes.
As x increases, the values of y increase more rapidly for higher bases. The graph of y = 4^x will be above the graph of y = 3^x, which in turn will be above the graph of y = 2^x.
You can use a graphing calculator or online graphing tools to plot these functions and explore different values of x and y.
1. Create a coordinate plane by drawing two perpendicular lines, one for the x-axis and one for the y-axis. Label the x-axis with "x" and the y-axis with "y".
2. Choose appropriate scales for the x- and y-axes. Since the graphs are exponential functions, it is recommended to use logarithmic scales to better visualize the differences in growth rates.
3. Plot the points for each function.
- For y = 2^x, calculate a few values of y for different values of x, such as (0, 1), (1, 2), (2, 4), and (3, 8). Plot these points on the graph.
- Repeat the process for y = 3^x and y = 4^x, calculating points such as (1, 3), (2, 9), and (3, 27) for y = 3^x, and (1, 4), (2, 16), and (3, 64) for y = 4^x.
4. Connect the points for each function with a smooth curve. The curve for y = 2^x will have a steep slope, while the curves for y = 3^x and y = 4^x will have less steep slopes.
As x increases, the values of y increase more rapidly for higher bases. The graph of y = 4^x will be above the graph of y = 3^x, which in turn will be above the graph of y = 2^x.
You can use a graphing calculator or online graphing tools to plot these functions and explore different values of x and y.
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