Answer:
[tex]\huge\boxed{[-5;\ -2)\ \cup\ [3;\ 13)}[/tex]
Step-by-step explanation:
The following piecewise functions are linear functions. The graph of any of them is a line segment.
We just need to calculate the value of the function at each end specified in the brace.
[tex]y=3x-2\ \text{if}\ -1\leq x<0[/tex]
Substitute x =-1 and x = 0:
[tex]x=-1\\y=3(-1)-2=-3-2=-5\\\\x=0\\y=3(0)-2=0-2=-2[/tex]
Range of this piece is [-5; -2)
[tex]y=2x+3\ \text{if}\ 0\leq x<5[/tex]
Substitute x =0and x = 5:
[tex]x=0\\y=2(0)+3=0+3=3\\\\x=5\\y=2(5)+3=10+3=13[/tex]
Range of this piece is [3; 13)
Therefore the range of the following piecewise function is:
[tex][-5;\ -2)\ \cup\ [3;\ 13)[/tex]
Look at the picture.
