Question

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

Answer 1

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

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 `x` and solve for `y`.

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 `x` values, while range is for `y`.

Because `x` can only be values that is equal to or greater than `2`, the domain is: `{x inRR | x >= 2/3}`

On the other hand, the range can only be values equal to or greater than `0`. Thus, the range is: `{y inRR | y >=0}`

Hope this helps :)