Question

What is the range of a function?

Answer 1

The range of a function is the set of all possible outputs of that function.

For example, let's look at the function `y = 2x`

Since we can plug in any x value and multiple it by 2, and since any number can be divided by 2, the output of the function, the `y` values, can be any real number.

Therefore, the range of this function is "all real numbers"

Let's look at something slightly more complicated, a quadratic in vertex form: `y=(x-3)^2+4`. This parabola has a vertex at `(3,4)` and opens upwards, therefore the vertex is the minimum value of the function. The function never goes below 4, therefore the range is `y>=4`.