Square Root Function Graph - Examples & Practice

Square Root Graph

We've seen how to graph different functions, like a linear function and a quadratic function. Most of these types of standard functions have parent graphs, which are basically graphs of the basic function. For example, we know that the parent function of a linear equation is $y=x$, where the line goes through the origin, (0,0), and has a slope of $1$. In this lesson, we will explore the parent function of another type of equation: the square root equation.

The base square root graph is: $y=\sqrt x$.

Notice it starts at the point $(0,0)$ and goes through the point $(1,1)$. The $x$ value continues to increase, and the $y$ value will plateau and increase infinitesimally.

Stretch and Shrink

Like other parent functions, we can also stretch or shrink the graph: $$y=a\sqrt x$$

• If $a$ is greater than $1$ ($a>1$) the graph gets stretched.
• If $a$ is between $0$ and $1$ ($0<a<1$) the graph gets shrunk.

You can also shift the graph to the left, right, up, and down. The best way to graph a square root function is to create a table of values, calculate coordinates, and plot a few points! Then, you can follow the points because you know what the general patten will be.

We can use this basis to solve word problems with radical equations!

(Video) Graphing the Square Root Function

by mathman1024

This video by mathman1024 explains graphing square root functions.

$\large{\text{Summary}}$

$$f(x)=\sqrt{x}$$

If we draw a t-table of values we get $$\begin{array}{c|c} x&y\\ \hline -1&\text{NA}\\ 0&0\\ 1&1\\ 2&1.414...\\ 4&2\\ 9&3 \end{array}$$

(Remember, you can't take the square root of a negative number.)

So now we plot these point on our graph.

Now we we connect these points we get the graph of the square root function!

As you can see the graph is only the positive $x$ and $y$ values. So we can define our domain and range as: $$D=[0,\infty)\\ R=[0,\infty)$$

Graphing Square Root Functions

Square root functions, $y=\sqrt{x}$, are very straightforward. Check out this graphic to understand what they look like and the key points to graphing square root functions.

These key points will stand true for all parent square root functions that take the form: $y=\sqrt{x}$.

You can also shrink or stretch a square root function!

$$y=a \sqrt{x}$$

,where $a$ can take any numerical value.