Question

what is the y-intercept of the function $g(x) = \sqrt3{x + 8}$? (1 point)
\bigcirc (0, 8)
\bigcirc (2, 0)
\bigcirc (0, 2)
\bigcirc (8, 0)

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \(y = g(x)\) is the point where \(x = 0\). So we substitute \(x=0\) into the function \(g(x)=\sqrt[3]{x + 8}\).

Step2: Substitute \(x = 0\) into the function

When \(x = 0\), we have \(g(0)=\sqrt[3]{0 + 8}\). Since \(\sqrt[3]{8}=2\) (because \(2\times2\times2 = 8\)), then \(g(0)=2\). So the y - intercept is the point \((0,2)\) because when \(x = 0\), \(y=g(0) = 2\).

Answer:

C. \((0,2)\) (assuming the options are labeled as A. \((0,8)\), B. \((2,0)\), C. \((0,2)\), D. \((8,0)\))