which is the graph of the cube root function $f(x)=sqrt3{x}$?
which is the graph of the cube root function $f(x)=sqrt3{x}$?
Answer
Explanation:
Step1: Analyze key - points of cube - root function
The cube - root function $y = \sqrt[3]{x}$ has the following properties: Its domain is all real numbers ($x\in(-\infty,\infty)$) and its range is also all real numbers ($y\in(-\infty,\infty)$). When $x = 0$, $y=\sqrt[3]{0}=0$, so the graph passes through the origin $(0,0)$. As $x$ increases, $y$ also increases, and as $x$ decreases, $y$ decreases.
Step2: Examine the given graphs
The first graph has a horizontal asymptote and is decreasing for positive $x$ values, which is not the behavior of the cube - root function. The second graph passes through the origin $(0,0)$ and increases as $x$ increases and decreases as $x$ decreases, which is consistent with the properties of the cube - root function $y = \sqrt[3]{x}$.
Answer:
The second graph.