Answer :
Answer:
The range of the function is represented by [tex]Ran\{f(x)\} = (-15, 12][/tex].
Step-by-step explanation:
Let be [tex]f(x) = -3\cdot x + 6[/tex], for [tex]x \in [-2,7)[/tex]. As we notice that [tex]f(x)[/tex] is an inyective function, that is, the inexistence of two or more domain element with the same image, with a monotone behavior, we can obtain the bounds of the range of the function by evaluating the expression:
Lower bound ([tex]x = -2[/tex])
[tex]f(-2) = -3\cdot (-2)+6[/tex]
[tex]f(-2) = 12[/tex]
Upper bound ([tex]x = 7[/tex])
[tex]f(7) = -3\cdot (7)+6[/tex]
[tex]f(7) = -15[/tex]
The range of the function is represented by [tex]Ran\{f(x)\} = (-15, 12][/tex]