Question

identify the equation for the graph. $y - 3 = sqrt3{x}$, $y + 3 = sqrt3{x}$, $y = sqrt3{x + 3}$

Explanation:

Step1: Recall the parent cube root function

The parent function is \( y = \sqrt[3]{x} \), which passes through the origin \((0,0)\).

Step2: Analyze the graph's shift

Looking at the given graph, when \( x = 0 \), let's find the \( y \)-value. From the graph, at \( x = 0 \), \( y=-3 \).

Step3: Test each equation at \( x = 0 \)

• For \( y - 3=\sqrt[3]{x} \): At \( x = 0 \), \( y-3 = 0\Rightarrow y = 3 \). Not matching.
• For \( y + 3=\sqrt[3]{x} \): At \( x = 0 \), \( y+3 = 0\Rightarrow y=-3 \). This matches the \( y \)-value at \( x = 0 \) from the graph.
• For \( y=\sqrt[3]{x}+3 \): At \( x = 0 \), \( y = 0 + 3=3 \). Not matching.

Answer:

\( y + 3=\sqrt[3]{x} \)