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.`

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.`