which graph represents $y = sqrt3{x}+2$?

Explanation:

Step1: Analyze key - points of the function

The parent function of $y = \sqrt[3]{x}+2$ is $y=\sqrt[3]{x}$. The graph of $y = \sqrt[3]{x}$ passes through the origin $(0,0)$ and has a domain and range of all real numbers. The function $y=\sqrt[3]{x}+2$ is a vertical shift of the function $y = \sqrt[3]{x}$ up by 2 units. So, when $x = 0$, $y=\sqrt[3]{0}+2=2$.

Step2: Check the graphs

We look for a graph that has a point at $(0,2)$ and has the general shape of a cube - root function. The cube - root function $y=\sqrt[3]{x}$ has a shape that increases slowly for positive $x$ and decreases slowly for negative $x$. A vertical shift up by 2 units means the new graph will have the same shape but all $y$ - values are 2 units higher than the $y$ - values of $y=\sqrt[3]{x}$.

Answer:

The graph that has the point $(0,2)$ and the shape of a cube - root function. (Since no specific options are labeled as A, B, C etc., we can't give a letter - based answer, but the above description helps in identifying the correct graph among the given ones).