Question

Determine the domain and range of the function f(x)= 3x+2. Also, state the intervals where the function f(x)= 3x+ 2 is increasing or decreasing.​

Answer 1

Increasing on it's domain
`(-\infty,\infty)` because the slope is positive.

The domain and range are both all real numbers, also known as

`(-\infty,\infty)`.

Explanation:

All domain really means is what numbers can you plug in and you get number back from your function.

I should be able to plug in any number into 3x+2 and result in a number. There are no restrictions for x on 3x+2.

The domain is all real numbers.

In interval notation that is
`(-\infty,\infty)`.

Now the range is the set of numbers that get hit by y=3x+2.

Well y=3x+2 is a linear function that is increasing. I know it is increasing because the slope is positive 3. I wrote out the positive part because that is the item you focus on in a linear equation to determine if is increasing or decreasing.

If slope is positive, then the line is increasing.

If slope is negative, then the line is decreasing.

So y=3x+2 hits all values of y because it is increasing forever. The range is all real numbers. In interval notation that is
`(-\infty,\infty)`.