The solution for this problem involves graphing the function f(x) = (3/2)^(-x), for the range of x from -10 to 10.
Here's a step-by-step guide:
1. Understand the Function: The first step in solving this is to understand what the function is. We're dealing with an exponential function where the base is (3/2) and the exponent is -x.
2. Identify the Key Properties: Exponential functions have certain characteristics. Since the base is greater than 1, and exponent is -x, we're dealing with a function that decreases as x increases. The function will never reach 0 and never go below the x-axis.
3. Determine the Range of X-Values: In this case, we're asked to plot the function between -10 to 10.
4. Plot the Points: You'll want to calculate the y-values of the function at several points within this range. As an example, when x = -10 the function will be y = (3/2)^10, and when x = 10, the function will be y = (3/2)^(-10). For best results, choose several values between -10 and 10 and calculate the corresponding y-values.
5. Draw the Graph: Once you have your points, plot them on the graph. Because this is an exponential function, it will begin high on the y-axis (for negative x-values), and then decrease toward the x-axis as x increases, but will never actually reach the x-axis.
6. Interpret the Graph: The graph should decrease toward the x-axis as x increases, as it represents a function that decreases as the input (x) increases. Because the base (3/2) is greater than 1, the function starts high and gradually decreases.
Remember, this type of function will always stay above the x-axis (y > 0) for every real number x. The reason is that any non-zero number to a power is always positive. This is a key feature of the graph of this function.