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#.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.