Question

determine the range and domain of the function f(x)=3x+4; x <0. f(x)=3x+6; x >/ 0

Answer 1

\[f(x)=\begin{cases}3x+4&\text{for }x<0\\3x+6&\text{for }x\ge0\end{cases}~~?\]

Answer 2

yes! @SithsAndGiggles

Answer 3

The domain is certainly all real numbers. Neither \(3x+4\) nor \(3x+6\) have any discontinuities, and both are defined at \(x=0\) (the cut-off for the given pieces of \(f(x)\)).

The range is slightly tricky. Normally, either line would take on all real numbers, but graphically, \(3x+6\) is a vertically shifted version of \(3x+4\):

Answer 4

However, according to the definition of \(f(x)\), you have the following graph:

(The scratched out portions are removed)