Question

This is algebra 2, function graphsI’m a little confused with how to start it out. ( I scribbled the black so you won’t get confused with the other problem)

Answer 1

Solution:

The graph shown is a graph of a square root function that has been transformed.

The parent square root function is;

$y=\sqrt[]{x}$

The graph of the parent function is as shown below;

The parent function occurs at;

$\begin{gathered} y=\sqrt[]{x} \\ It\text{ occurs at (0,0)} \end{gathered}$

Comparing the parent function to the images in the question.

The red image originates at,

$(-3,-3)$

This shows the parent function is translated 3 units to the left on the x-axis and 3 units down from its original position on the y-axis.

Therefore, the equation of the red image is given below;

$\begin{gathered} y=\sqrt[]{x} \\ \\ \text{The equation of the red image translated from the parent function is;} \\ y=\sqrt[]{x+3}-3 \end{gathered}$

The graph is as shown below;

The green image originates at,

$(3,3)$

This shows the parent function is translated 3 units to the right on the x-axis and 3 units up from its original position on the y-axis.

Therefore, the equation of the green image is given below;

$\begin{gathered} y=\sqrt[]{x} \\ \\ \text{The equation of the gr}een\text{ image translated from the parent function is;} \\ y=\sqrt[]{x-3}+3 \end{gathered}$

The graph is as shown below;