Question

Which of the following functions is graphed below.

Answer 1

Answer: Option A

$y=\left \{ {{x^2 +2;\ \ x<1 \atop {-x+2;\ \ x\geq1}} \right.$

Step-by-step explanation:

In the graph we have a piecewise function composed of a parabola and a line.

The parabola has the vertex in the point (0, 2) and cuts the y-axis in y = 2.

The equation of this parabola is $y = x ^ 2 +2$

Then we have an equation line$y = -x + 2$

Note that the interval in which the parabola is defined is from -∞ to x = 1. Note that the parabola does not include the point x = 1 because it is marked with an empty circle " о ."

(this is $x< 1$)

Then the equation of the line goes from x = 1 to ∞ . In this case, the line includes x = 1 because the point at the end of the line is represented by a full circle .

(this is $x\geq 1$)

Then the function is:

$y=\left \{ {{x^2 +2;\ \ x<1 \atop {-x+2;\ \ x\geq1}} \right.$