Question

Is the function `f(x) = (18)^x` increasing or decreasing?

Answer 1

depend on the value of `x`. See explanation

Explanation:

if `x -> x>1` then `18^x` is increasing as `x` increases

if `x -> 0 < x <1` then `18^x` is decreasing as `x` approaches 0 from the positive side.

If `x` is negative then we have `1/(18^x)` so:

If `x -> (-1) < x < 0` then as `x` approaches 0 the `18^x` in `1/(18^x)` gets smaller and smaller so `1/18^x` gets bigger and bigger

If `x -> x < (-1)` then the `18^x` in `1/(18^x)` gets bigger and bigger as `x` becomes increasingly les -1. So `1/(18^x)` becomes less and less.

Answer 2

The function is increasing.

Explanation:

An exponential function `y=a^x` is :

• increasing for `a>1`
• decreasing for `a in (0;1)`
• not defined for `a<0` (because negative numbers cannot be raised to rational powers `(-1)^(1/2)=sqrt(-1)` is not a real number)