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

Question

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

anonymous · Answer

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

anonymous · Answer

yes! @SithsAndGiggles

anonymous · Answer

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 $3x+4$:
|dw:1411004866414:dw|

anonymous · Answer

However, according to the definition of $f(x)$, you have the following graph:
|dw:1411004939424:dw|
(The scratched out portions are removed)