Question

describe how the graph of $g(x)=\sqrt3{x}+2$ can be obtained from the graph of $f(x)=\sqrt3{x}$. then graph the function $g(x)$... how can the graph of $g(x)=\sqrt3{x}+2$ be obtained from the graph of $f(x)=\sqrt3{x}$? \\(\bigcirc\\) a. shift the graph 2 units right. \\(\bigcirc\\) b. shift the graph 2 units up \\(\bigcirc\\) c. shift the graph 2 units down \\(\bigcirc\\) d. shift the graph 2 units left

Explanation:

To determine how the graph of \( g(x)=\sqrt[3]{x}+2 \) is obtained from \( f(x)=\sqrt[3]{x} \), we use the concept of vertical shifts in function transformations. For a function \( y = f(x)+k \), if \( k>0 \), the graph of \( f(x) \) is shifted \( k \) units up. Here, \( g(x)=f(x) + 2 \) (since \( f(x)=\sqrt[3]{x} \) and \( g(x)=\sqrt[3]{x}+2 \)), so \( k = 2>0 \), meaning we shift the graph of \( f(x) \) 2 units up.

Answer:

B. Shift the graph 2 units up