Is f(x) = -2^x a negative exponential function?

Question

Can exponential function be both negative and positive?

Answer 1

No. It is true that the values of -2^x are always negative, because 2^x is always positive and -2^x means -(2^x). However, this is not what is called a "negative exponential function." A function of the form A*b^x is always an "exponential function," even when A is negative. A negative exponential function requires the form A*b^(-x). It is the exponent that needs to be negative in order to have a negative exponential function. You could call -2^x a "negative-valued exponential function" if you wanted to.

Answer 2

In this case, yes, we have a negative exponential function.
Since 2^x must be non-negative, it approaches 0 asymptotically as x-> -infinity, it crosses y=1 when x=0 and blows up as x->+infinity, y=-(2^x) must be a reflection of y=(2^x) about the x-axis.

To clarify this, as x-> -infinity, y=-(2^x) approaches zero from the negative half of the y-axis, it crosses y=-1 at x=0 and it goes to some large negative value as x gets bigger and bigger in the positive direction.

Answer 3

This is not bad form at all as people think, it is just that they do not know the order of operations. By the way, you are wrong to call this an exponential function. 5²x - 1 = 7 25x - 1 = 7 25x = 8 x = 8 / 25

Answer 4

-(2^x) it is always negative