Question

6.5 graphing and solving exponential functions quiz

the asymptote of \\(f(x)=4^x\\) is =

Explanation:

Identify the function type

Using the Exponential Growth knowledge point
The given function is \(f(x) = 4^x\). This is a basic exponential function where the base is \(4 > 1\), representing exponential growth.

Determine the behavior as x approaches negative infinity

Using the Exponential Growth knowledge point
As \(x \to -\infty\), the term \(4^x \to 0\). Specifically, \(4^{-1} = 0.25\), \(4^{-2} = 0.0625\), and so on, approaching \(0\) but never reaching it.

Find the horizontal asymptote

Using the Horizontal Lines knowledge point
Since \(f(x) \to 0\) as \(x \to -\infty\), the graph of the function approaches the horizontal line \(y = 0\). Therefore, the horizontal asymptote is \(y = 0\).

Answer:

The asymptote of \(f(x)=4^x\) is <blank>\(y\)</blank> = <blank>\(0\)</blank>