Question

Write an equation of a piecewise defined function with the given conditions: domain is (-3, 2) u (2, ∞) range is (-1, ∞) function must have only two pieces

Answer 1

$\left \{ {{f(x)=x+2, -3\ \textless \ x\ \textless \ 2} \atop {f(x)=x-2, 2\ \textless \ x\ \textless \ infinity}} \right.$

f(x) has to be close to -1 when x is close to -3, and so f(x) is increasing when x increases, and there are no numbers from -1 to ∞ that there is no f(x) value. In the first piece of the function f(x) ranges from -1 to 4 and the second piece from 0 to ∞ so. The ranges had to overlap since it's not defined at x = 2.