Question

Not an actual test question but just curious:

Answer 1

well, when we use the word "the function" we're referring to the dependent part, which depends on the independent, y,x wise, we're referring to the function "y" or f(x) if you wish.

so for an exponential function

is the function ever positive only? it can be

is it negative only?  it can be

can it be both?  sure thing, most of the time it's both

we can say a function f(x) is always positive when the independent values of "x" yield a positive value only, mind you that when we're talking about "the function" we're really referring to the resulting values in a set, so can the values of the output no matter what "x" we use be always positive? sure, can they also be negative only? sure, how about both? sure thing.

notice the template in the picture below, we can transform any exponential function like the one above 2ˣ with some vertical shift upwards, and is always positive, or -2ˣ with a vertical shift downwards and it's always negative, or we can stretch it about and have -2ˣ shifted upwards so sometimes is positive, and sometimes is negative.

above the x-axis is always positive, below is negative, but with transformations on the parent function it can be any of the three types.