Question

Which of the following functions is graphed below ?

Answer 1

A)
`\displaystyle y=\left \{ {{x^3-4,\,x\leq 1} \atop {x^2-3,\,x > 1}} \right.`

Explanation:

The first "piece" of the piecewise function,
`y=x^3-4`, contains
`x=1` because of the closed dot there.

The second "piece" of the piecewise function,
`y=x^2-3`, doesn't contain
`x=1` because of the open dot there.

What occurs between the two pieces is called a jump discontinuity.

Therefore, A is the correct answer.