Precalculus Examples

$(0, 0)$ , $(- 6, 6)$

Step 1

Since for each value of $x$ there is one and only one value of $y$ , the given relation $(0, 0), (- 6, 6)$ is a function.

The relation is a function.

Step 2

Since the relation is a function and for each value of $y$ there is one and only one value of $x$ , the given relation $(0, 0), (- 6, 6)$ is a one-to-one function.

The relation is a one-to-one function.

Step 3

Every point in the range is the value of $y$ for at least one point $x$ in the domain, so this is a surjective function.

Surjective function

Step 4

Since $(0, 0), (- 6, 6)$ is injective (one to one) and surjective, then it is bijective function.

Bijective function