Answer: False
Solution:
The exponential functions with the form y=a^x never cross the x-axis (x-axis is an asymptote), but in this case we have the exponential function translated 4 units downward, then this function crosses the x-axis.
As it is not given a is positive real number or negative real number.
By supposing a is any real number, we will draw the graph of the curve
[tex]a^x-4[/tex] by taking different values of x.
As i have taken different values of a ,
I found that for a< 0, the graph of the curve [tex]y=a^x-4[/tex] does not exist.
For any other value of a, the curve cuts the x axis at one point.
For values of 1<a<0, the curve will cut negative side of X axis.
For value of a, a≥1, the curve will cut positive side of X axis.
For , a=0, the curve will not cut the x axis.
So, The function , f(x)=[tex]a^x -4[/tex] will cuts the x axis at one point for a >0 and for negative values of a, and for a< 0 ,it will not cut the x axis.
