which is the graph of $f(x)=sqrt3{x}-4$?
which is the graph of $f(x)=sqrt3{x}-4$?
Answer
Explanation:
Step1: Analyze the parent - function
The parent - function of $y = \sqrt[3]{x}-4$ is $y=\sqrt[3]{x}$. The domain of $y = \sqrt[3]{x}$ is all real numbers ($x\in(-\infty,\infty)$), and its range is also all real numbers ($y\in(-\infty,\infty)$). The graph of $y = \sqrt[3]{x}$ passes through the origin $(0,0)$.
Step2: Analyze the transformation
The function $y=\sqrt[3]{x}-4$ is a vertical translation of the function $y = \sqrt[3]{x}$ down by 4 units. So, when $x = 0$, $y=\sqrt[3]{0}-4=-4$. The graph of $y=\sqrt[3]{x}-4$ passes through the point $(0, - 4)$.
Answer:
The second graph (the one where the curve passes through the point $(0,-4)$)