23 mark for review the function f is given by f(x)=−3log₂x + 1. which of the following limit statements…

23 mark for review the function f is given by f(x)=−3log₂x + 1. which of the following limit statements describe the end - behaviors of f? a lim x→1⁺ f(x)=−∞ and lim x→∞ f(x)=∞ b lim x→1⁺ f(x)=∞ and lim x→∞ f(x)=−∞ c lim x→0⁺ f(x)=−∞ and lim x→∞ f(x)=∞ d lim x→0⁺ f(x)=∞ and lim x→∞ f(x)=−∞

23 mark for review the function f is given by f(x)=−3log₂x + 1. which of the following limit statements describe the end - behaviors of f? a lim x→1⁺ f(x)=−∞ and lim x→∞ f(x)=∞ b lim x→1⁺ f(x)=∞ and lim x→∞ f(x)=−∞ c lim x→0⁺ f(x)=−∞ and lim x→∞ f(x)=∞ d lim x→0⁺ f(x)=∞ and lim x→∞ f(x)=−∞

Answer

Explanation:

Step1: Analyze $\lim_{x\rightarrow0^{+}}f(x)$

As $x\rightarrow0^{+}$, $\log_{2}x\rightarrow-\infty$. Then $- 3\log_{2}x\rightarrow\infty$ and $f(x)=-3\log_{2}x + 1\rightarrow\infty$.

Step2: Analyze $\lim_{x\rightarrow\infty}f(x)$

As $x\rightarrow\infty$, $\log_{2}x\rightarrow\infty$. Then $-3\log_{2}x\rightarrow-\infty$ and $f(x)=-3\log_{2}x + 1\rightarrow-\infty$.

Answer:

D. $\lim_{x\rightarrow0^{+}}f(x)=\infty$ and $\lim_{x\rightarrow\infty}f(x)=-\infty$