Find the range of the following peicewise function

Range are the y-values. Plug the x-values into the equation and solve for y.

f(x) = 3x - 2

f(-1) = 3(-1) - 2

     =   -3  - 2

     = -5

f(0) = 3(0) - 2

     =   0  - 2

      = -2

R: -5 ≤ y < -2   ⇒   [-5, -2)

f(x) = 2x + 3

f(0) = 2(0) + 3

     =   0  + 3

     =    3

f(5) = 2(5) + 3

      =  10 + 3

      =  13

R: 3 ≤ y < 13    ⇒  [3, 13)

Now, put them together:  [-5, -2) U [3, 13)

A

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