Question

Please help.

choose the definition for the function.

Answer 1

Answer: Choice A

`y = \begin{cases}{x+1 \ \ x \le 2\\ x+2 \ \ x > 2\end{cases}`

All four answer choices have an "x+1" and "x+2" as part of the piecewise definition. The only differences are that the inequalities are set up slightly different from one another. The inequalities determine which equation is graphed.

The left part of the piece-wise graph given is the equation y = x+1 but only when x is 2 or smaller. So only when
`x \le 2`. Note the closed or filled in circle at the endpoint for this left piece.

The right piece has an open circle meaning we do not include x = 2 here. So we go with x > 2 instead of
`x \ge 2`

Choices C and D are not possible because x = 2 would lead to more than one output. In other words, we wouldn't have a function here since it fails the vertical line test. Choice B would only be valid if the open and closed endpoints were swapped.