Question

PLEASE HELP Which of the following functions is graphed below??

Answer 1

The graph is
$y = { \{x}^{2} + 2 \: . \: x \leqslant 1 \\ { \{ - x} + 2 \: . \: x > 1$
Sorry - I'm not really sure how to format the function properly, the '.' stands for a comma

Answer 2

Answer:

$y=\left \{ {{x^2+2,\:x\:<\:1} \atop {-x+2,\:x\ge1}} \right.$

Step-by-step explanation:

The graph is a piece-wise function.

It is made up of a quadratic function and a linear function.  

The quadratic function is $y=x^2+2$ and the linear function is $y=-x+2$.

The graph of the quadratic function is defined on the  interval $x\:<\:1$ and the graph of the linear function is defined on the interval $x\ge 1$.

So in short, if $\:x\:<\:1$, then $y=x^2+2$, else, $y=-x+2$.

Writing these two functions as a single piece-wise function gives,

$y=\left \{ {{x^2+2,\:x\:<\:1} \atop {-x+2,\:x\ge1}} \right.$

The correct answer is C.