Exploring the Exponential Function f(x) = 5(2)^x | Evaluating and Graphing

f(x) = 5(2)^x

Let’s start by understanding the given function

Let’s start by understanding the given function.

The function is written as f(x) = 5(2)^x. This is an exponential function, with a base of 2 raised to the power of x, multiplied by 5.

An exponential function has the general form of f(x) = a(b)^x, where “a” is a constant multiplier and “b” is the base of the exponent. In this case, a = 5 and b = 2.

To evaluate this function, you can substitute different values of x into the equation and calculate the corresponding y-values.

For example, let’s find f(0):
f(0) = 5(2)^0
f(0) = 5(1)
f(0) = 5

Similarly, let’s find f(1):
f(1) = 5(2)^1
f(1) = 5(2)
f(1) = 10

Now, let’s plot these points on a graph. Here are a few more points to help visualize the graph:

f(-1) = 5(2)^(-1) = 5/2 = 2.5
f(2) = 5(2)^2 = 5(4) = 20
f(3) = 5(2)^3 = 5(8) = 40

The graph of the function will show an exponential growth pattern, as the base (2) is greater than 1. As x increases, the value of f(x) will increase rapidly.

Note that the function may also take negative values for non-integer values of x, as (2)^x for negative x-values results in fractions or decimals.

I hope this explanation helps you understand the given exponential function. If you have any further questions, feel free to ask!

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