Question

Choose the end behavior of the following function f(x) = 4^x-3 -2

Answer 1

Determine the value of the expression for x tends to infinity.

`\begin{gathered} \lim _(x\to\infty)(4^(x-3)-2)=\lim _(x\to\infty)4^(x-3)-\lim _(x\to\infty)2 \\ =\infty-2 \\ =\infty \end{gathered}`

Determine the value of expression for x tends to negative infinity.

`\begin{gathered} \lim _(x\to-\infty)(4^(x-3)-2)=\lim _(x\to-\infty)4^(x-3)-\lim _(x\to-\infty)2 \\ =0-2 \\ =-2 \end{gathered}`

So answer is,

`\begin{gathered} \text{As x}\rightarrow-\infty,\text{ f(x)}\rightarrow-2 \\ \text{As x}\rightarrow\infty,\text{ f(x)}\rightarrow\infty \end{gathered}`

Option B is correct