describe the end behavior of the graph of the function.\n\n$f(x)=4(4)^{-x}+9$\n\nas $x\\to…

Explanation:

Step1: Analyze (x\to-\infty)

When (x\to-\infty), (-x\to\infty). For the exponential function (y = a^{u}) ((a = 4>1), (u=-x)), as (u\to\infty), (4^{-x}=4^{u}\to\infty). Then (f(x)=4(4)^{-x}+9). Multiply by (4) and add (9), so (f(x)=4\times\infty + 9=\infty)

Step2: Analyze (x\to\infty)

When (x\to\infty), (-x\to-\infty). For the exponential function (y = a^{u}) ((a = 4>1), (u =-x)), as (u\to-\infty), (4^{-x}=\frac{1}{4^{x}}\to0). Then (f(x)=4\times0 + 9=9)

Answer:

As (x\to-\infty), (f(x)\to\infty); As (x\to\infty), (f(x)\to9)