Determine the value of the expression for x tends to infinity.
[tex]\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}[/tex]
Determine the value of expression for x tends to negative infinity.
[tex]\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}[/tex]
So answer is,
[tex]\begin{gathered} \text{As x}\rightarrow-\infty,\text{ f(x)}\rightarrow-2 \\ \text{As x}\rightarrow\infty,\text{ f(x)}\rightarrow\infty \end{gathered}[/tex]
Option B is correct
