# How do you find the domain and range of #f(x)=sqrt(3x-2)#?

##### 1 Answer

Visualize the graph (often easier by graphing the function). Then, determine all possible values of

#### Explanation:

Let's list the transformations of the function before we graph it out. By graphing it out, we get a visual of the function so it's much easier to determine the domain and range.

- Horizontal compression by a factor of
#1/3# . - Horizontal translation requires us to isolate
#x# within the radical. We get#2/3# to the right.

Now let's graph this.

The easiest way to do this is to sub in values for

You get this:

graph{y=sqrt(3x-2) [-10, 10, -5, 5]}

Now we can visually see the function's domain and range.

The domain is a set of all the possible

Because

On the other hand, the range can only be values equal to or greater than

Hope this helps :)