2 Answers

Lapurita · Answer 1 · 2019-02-17T18:17:31+0000

Answer:

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

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.

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