Question

If we are given a function and it is raised to the second power, why is it still considered a function even though functions are supposed to be raised to the first power?

Answer 1

Even functions raised to the second power are still considered functions because the power rule can be applied to any function. Each term in the function is raised to the power, resulting in a squared function. Functions can be raised to powers other than one and are still considered functions.

Step-by-step explanation:

An even function raised to the second power is still considered a function because the power rule can be applied to any function, regardless of whether it is raised to the first power or any other power. The power rule states that when a function is raised to a power, each term in the function is raised to that power.

For example, if we have the function f(x) = x^2, raising it to the second power gives us f(x)^2 = (x^2)^2 = x^4. The function is still a function, but now each term in the function has been squared.

So, even though functions are typically shown raised to the first power, they can still be raised to other powers and are still considered functions.