Hi there!
An exponential function mostly has the following form:
[tex]y = a(b) {}^{x} [/tex]
In this function x is the variable. Whatever value of x you fill in, the outcome for y will always be greater than 0. Since this outcome is always greater than zero, the function doesn't cross the x-axis.
Let's have a look at the examples from the picture. We can see two exponential formulas. Whatever value of x you fill in (no matter how big) at the blue formula ( y = 0.5 ^ x ), the value of y will only become smaller and smaller, but will never be 0. Therefore, the line doesn't cross the x-axis.
The other line works the exact same way. Whatever value of x you fill in (no matter how small -- even including negative) at the red formula ( y = 2 ^ x ), the value of y will only become smaller and smaller, but will never be 0. Therefore, the line doesn't cross the x-axis.
