Question

What is the range of the function `y=8x-3`?

Answer 1

Range of `y` is `(-oo,+oo)`

Explanation:

`y=8x-3`

First note that `y` is a straight line with slope of `8` and `y-`intercept of `-3`

The range of a function is the set of all valid outputs ("`y-` values") over its domain.

The domain of all straight lines (other than the vertical ones) is `(-oo,+oo)` since they are defined for all values of `x`

Hence, the domain of `y` is `(-oo,+oo)`

Also, since `y` has no upper or lower bounds, the range of `y` is also `(-oo,+oo)`

Answer 2

`-oo<=y<=oo` (all real numbers (`R`))

Explanation:

Just remember that the range for a linear function is always all real numbers unless it is horizontal (doesn't have `x`).

One example of a linear function with a range of not all real numbers would be `f(x)=3`. The range for this function would be `y=3`.

I hope that helps!