is y=2^-x a function?if so, what kind of function is it?

y=2^(-x)

It is a function because it passes the vertical line test.
It is an exponential funciton.
Note the ^ (exponential operator).

Yes, the equation y = 2^(-x) represents a function.

This function is known as an exponential function. It has a base of 2 and an exponent of -x. In this case, as x increases, the exponent becomes more negative. This causes the function to approach 0 as x approaches infinity.

The graph of an exponential function with a negative exponent will also have certain characteristics. It will be defined for all real numbers, and the graph will gradually approach the x-axis as x increases. The function will be decreasing from left to right, meaning that as x increases, y decreases.

To determine whether the equation y = 2^(-x) represents a function, we need to check whether there is a unique y-value corresponding to each x-value or if the same x-value has multiple y-values.

In this case, we can see that as the x-value changes, the exponent of 2 changes. However, no matter what value x takes, 2^(-x) will always be a single real number, so there is only one corresponding y-value for each x-value. Therefore, y = 2^(-x) is indeed a function.

As for the type of function, y = 2^(-x) represents an exponential function. It is a special type of exponential function called an exponential decay function because the base, 2, is greater than 1, and as x increases, the y-values approach zero. This means that the graph of y = 2^(-x) will show a decreasing curve that approaches the x-axis but never touches it.