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

1 Answer
Ryuu
Nov 7, 2017

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 :)

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