which graph represents $y = sqrt3{x - 5}$?
which graph represents $y = sqrt3{x - 5}$?
Answer
Explanation:
Step1: Analyze the parent - function
The parent - function of $y = \sqrt[3]{x - 5}$ is $y=\sqrt[3]{x}$, which has a domain of all real numbers and passes through the origin $(0,0)$.
Step2: Determine the transformation
The function $y=\sqrt[3]{x - 5}$ is a horizontal shift of the parent - function $y=\sqrt[3]{x}$ to the right by 5 units. When $x = 5$, $y=\sqrt[3]{5 - 5}=0$. So the graph of $y=\sqrt[3]{x - 5}$ passes through the point $(5,0)$.
Answer:
The graph that passes through the point $(5,0)$ and has the general shape of a cube - root function (smooth and increasing for all real $x$ values) is the correct one. Without seeing all the options, we can't specifically pick an option from a list, but the key characteristic is that it should be the cube - root function shifted 5 units to the right.