Question

Is it true that y=(a^x)-4 will never cross the x-axis?

Answer 1

When the function cross the X-Axis, the value of y must be zero. So, the question is whether y can ever be zero. Think of values of "a" and "x" that can make y zero. If you can't think of any, then the answer is true. Otherwise, false.

Answer 2

We need to know some condition of a, and x.
If we solve : a^x - 4 = 0
=> a^x = 4,
there are a few solution of x, one is when a = 2 & x = 2.
Hence the original statement is not always true