Question

The function f(x)=a^x-4 will never cross the x-axis. true or false

Answer 1

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

$a^x-4$ 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 $y=a^x-4$  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)=$a^x -4$ 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.

Answer 2

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.