Question

How do you use the vertical line test to show `y=3- sqrt(x+2)` is a function?

Answer 1

There are no `(x, y_1), (x, y_2)` on the graph`(f)` such that `y_1 \ne y_2`

Explanation:

We want to show that if `(x,y_1) \in \Gamma (f)` and `(x,y_2) \in \Gamma (f)` then `y_1 = y_2`

`y_1 = 3 - sqrt(x + 2)`

`y_2 = 3 - sqrt(x + 2)`

`y_1 - y_2 = 3 - 3 = 0`

`y_1 = y_2`