Q6. - Algebra 1

Question

Graph each function. Compare to the parent graph. State the domain and range.

$y=2\sqrt{x-2}$

Step-by-Step Solution

Answer

The graph of the given function $y=2\sqrt{x-2}$ is:

The parent graph is graph of $y=\sqrt{x}$. The graph of the function $y=2\sqrt{x-2}$ is obtained by shifting the graph of the function $y=\sqrt{x}$ horizontally right by 2 units and stretching the graph vertically by 2 units.

 

The domain of the given function $y=2\sqrt{x-2}$ is $x\in \left[2,\infty \right)$.

 

The range of the given function $y=2\sqrt{x-2}$ is $y\in \left[0,\infty \right)$.

Step 1. Graph the given function y = 2 x − 2 .

Make a table for values of $x$ and $y$.

$x$	$y=2\sqrt{x-2}$
2	$y=2\sqrt{2-2}=0$
3	$y=2\sqrt{3-2}=2$
6	$y=2\sqrt{6-2}=4$
11	$y=2\sqrt{11-2}=6$

Draw the graph of the function $y=2\sqrt{x-2}$ by using the table for values of $x$ and $y$.

Step 2. Compare the graph of the function y = 2 x − 2 with the parent graph.

The parent function is $y=\sqrt{x}$.

The graphs of the function $y=2\sqrt{x-2}$ and $y=\sqrt{x}$ are:

From the graphs of the function $y=2\sqrt{x-2}$ and $y=\sqrt{x}$, it can be noticed that the graph of the function $y=2\sqrt{x-2}$ is obtained by shifting the graph of the function $y=\sqrt{x}$ horizontally right by 2 units and stretching the graph vertically by 2 units.

Step 3. State the domain and range of the function y = 2 x − 2 .

The domain is the set of values of independent variable for which the function is defined and range is the set of values of dependent variable which is obtained by substituting the values of independent variable which are in the domain of the function.

In the function $y=2\sqrt{x-2}$, $x$ is the independent variable and $y$ is the dependent variable. Therefore, domain of the function $y=2\sqrt{x-2}$ is the set of values of $x$ for which the function is defined and range of the function $y=2\sqrt{x-2}$ is the set of values of $y$ which is obtained by substituting the values of $x$ which are in the domain of the function.

Therefore, the domain of the function $y=2\sqrt{x-2}$ is $x\in \left[2,\infty \right)$ and range of the function $y=2\sqrt{x-2}$ is $y\in \left[0,\infty \right)$.