Question

Which of the following functions is graphed below?86a.-82468-6-4-20-2-46-81x2 +2. x<1O A.y-1-x+2, X21O B. v- {**+2.x211-x+ 2 x 1O c. v - (x + 2 x 51|-x+2, *> 1D. y - {**+2x > 1|-*+2, 21

Answer 1

The circles bounding a graph can tell us the boundary of the graph, based on its shading or lack thereof.

If the circle is shaded, the position of the circle is included in the graph, that is:

`\begin{gathered} x\ge c\text{ }or\text{ }x\le c \\ \text{where} \\ c=\text{ Location of the circle} \end{gathered}`

If the circle is unshaded, the position of the circle is not included in the graph, that is:

The quadratic graph is bounded by an unshaded circle at x = 1. Since the graph is plotted at x < 1, then the function and its boundary are:

`y=x^2+2,x<1`

The linear graph is bounded by a shaded circle at x = 1. Since the graph is plotted at x > 1, then the function and its boundary are:

`y=-x+2,x\ge1`

Therefore, the correct option is OPTION A.