Question

Can someone help me with 1c? I don’t understand how to find an equation for an asymptote.

Answer 1

y = 0

Explanation:

1 c.

If we have an exponential function of the form
`f(x)=a^x`, where "a" is any positive integer, say, then that function will take the general shape of the function shown in the picture.

It will always approach the x-axis but never meet (touch). Any line that a function (graph) approaches but never touches, is known as an asymptote to the graph.

Since the function
`f(x)=4^x` follows the path of the general form shown above, this also approaches the x-axis, but never touches. So, the x-axis is the asymptote of the function.

We know

x-axis has equation y = 0, and

y-axis has equation x = 0

Here, the x-axis is the asymptote, so the equation is:

y = 0