Understanding Exponential Functions | Breaking Down the expression f(x) = 4(4)^x

f(x) = 4(4)^x

The expression f(x) = 4(4)^x represents a exponential function

The expression f(x) = 4(4)^x represents a exponential function. Let’s break it down:

First, let’s focus on the base of the exponential function, which is 4. In this case, the base is a positive number greater than 1. This means that as x increases, the value of the function will grow rapidly. Similarly, as x decreases, the value of the function will shrink very quickly.

Inside the parentheses, we have 4^x. This means that the base (4) is raised to the power of x. The exponent x determines the behavior of the function. If x is a positive integer, it represents the number of times the 4 will be multiplied by itself (e.g., 4^3 = 4 × 4 × 4 = 64). If x is a negative integer, it represents the reciprocal of the positive exponent (e.g., 4^(-2) = 1 / (4^2) = 1 / (4 × 4) = 1/16). If x is a non-integer or a fraction, then the exponential function will yield a value between the exponential values.

Finally, the entire expression is multiplied by 4, resulting in f(x) = 4(4^x). This means that each resulting value of 4^x will be multiplied by 4. The multiplication by 4 serves as a scaling factor and enlarges or shrinks the values of the exponential function.

To determine the values of the function for different inputs of x, you can substitute different values into the equation. For example, if we substitute x = 0, we have f(0) = 4(4^0) = 4(1) = 4. If we substitute x = 1, we have f(1) = 4(4^1) = 4(4) = 16.

I hope this explanation helps you understand the given exponential function. If you have any further questions or need additional clarification, please let me know!

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