which is the graph of $f(x)=-sqrt3{x}$?
which is the graph of $f(x)=-sqrt3{x}$?
Answer
Explanation:
Step1: Analyze domain
The cube - root function $y = \sqrt[3]{x}$ has a domain of all real numbers, and so does $y=- \sqrt[3]{x}$.
Step2: Analyze end - behavior
As $x\to+\infty$, $\sqrt[3]{x}\to+\infty$, then $y =-\sqrt[3]{x}\to-\infty$. As $x\to-\infty$, $\sqrt[3]{x}\to-\infty$, then $y =-\sqrt[3]{x}\to+\infty$.
Step3: Analyze key points
When $x = 0$, $y=-\sqrt[3]{0}=0$.
The graph that has the above - described properties (passes through the origin $(0,0)$, goes to positive infinity as $x$ goes to negative infinity and to negative infinity as $x$ goes to positive infinity) is the third graph.