Question

the parent function $y = \sqrt3{x}$ and a transformed function $y = \sqrt3{x - 1} + 3$ are shown on the coordinate plane.
complete the sentence to describe the graph of the transformed function compared with the parent function.
enter your answers in the boxes.
the graph of the parent function $y = \sqrt3{x}$ is translated $\square$ unit(s) right and $\square$ unit(s) up to graph the transformed function $y = \sqrt3{x - 1} + 3$.

Explanation:

Step1: Analyze horizontal translation

For a function \( y = f(x - h) \), the graph is translated \( h \) units to the right. Here, the parent function is \( y=\sqrt[3]{x} \) and the transformed function has \( x - 1 \), so \( h = 1 \), meaning 1 unit right.

Step2: Analyze vertical translation

For a function \( y = f(x)+k \), the graph is translated \( k \) units up. Here, the transformed function has \( + 3 \), so \( k = 3 \), meaning 3 units up.

Answer:

The graph of the parent function \( y=\sqrt[3]{x} \) is translated \(\boldsymbol{1}\) unit(s) right and \(\boldsymbol{3}\) unit(s) up to graph the transformed function \( y=\sqrt[3]{x - 1}+3 \).