Final answer:
To graph the function f(x) = 5(2)^x, label the axes, calculate and plot points for several x values, and draw an increasing curve through these points. The resulting graph is an exponential growth curve, which never intersects the x-axis.
Step-by-step explanation:
The question pertains to graphing the exponential function f(x) = 5(2)^x. To graph this function, one must recognize that it is an exponential growth function since the base (2) is greater than 1. As x increases, f(x) will increase exponentially. To draw this graph, you should follow these steps:
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- Label the x-axis (horizontal) and y-axis (vertical) and scale them appropriately based on the range of x values being considered and the expected range of f(x) values.
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- Begin by plotting the point where x=0; since any number to the power of 0 is 1, f(0) will be 5 * 1 = 5.
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- Choose a few more values of x (such as 1, 2, 3, ...) and calculate the corresponding f(x) values to plot additional points (for example, f(1) = 5 * 2 = 10, f(2) = 5 * 4 = 20, and so on).
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- Once you have plotted a sufficient number of points, draw a smooth curve that passes through all the points, which should be rising rapidly to the right, reflecting the exponential growth.
Remember, the graph should be increasing continuously and will never touch the x-axis as it approaches it asymptotically. You should not see a downward trend because it is an increasing exponential function.