## f(x) = 0.5(4)^x

### Sure, I’d be happy to help! The equation you provided, f(x) = 0

Sure, I’d be happy to help! The equation you provided, f(x) = 0.5 * (4)^x, represents a mathematical function. Let’s break it down and understand its components.

1. f(x): This notation represents the function itself. It means that the value of the function depends on the value of x. So, whenever we see f(x), we can substitute the input x to get the corresponding output of the function.

2. (4)^x: Inside the brackets, we have the number 4 raised to the power of x. This means that 4 is the base, and x represents the exponent. To simplify, we can think of it as 4 multiplied by itself x times.

3. 0.5 * (4)^x: This is the entire formula for the function. It states that the output of the function is equal to 0.5 multiplied by 4 raised to the power of x.

Now, let’s see how this function behaves when we substitute different values for x.

– When x = 0: If we plug in x = 0 into the function, we get f(0) = 0.5 * (4)^0 = 0.5 * 1 = 0.5. So, the output when x is zero is 0.5.

– When x = 1: Plugging in x = 1 gives us f(1) = 0.5 * (4)^1 = 0.5 * 4 = 2. Hence, the output when x is equal to 1 is 2.

– When x = -1: Here, we have a negative exponent. f(-1) = 0.5 * (4)^(-1) is equivalent to 0.5 * 1/(4^1), which simplifies to 0.5 * 1/4 = 0.5 * 0.25 = 0.125. Therefore, the output when x is -1 is 0.125.

– For other values of x: We can continue substituting different values for x to find their corresponding outputs.

This function represents exponential growth because the base (4) is greater than 1. As x increases, the function values will increase rapidly. As x approaches negative infinity, the function values will tend towards zero. Conversely, as x approaches positive infinity, the function values will grow exponentially.

I hope this explanation helps you understand the given equation better. If you have any more questions, please feel free to ask!

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