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Given the function f\left(x\right)=-3x+6f(x)=−3x+6 with a domain of [-2, 7), identify the range of the function using same notation.

User Dylan Karr
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Answer:

The range of the function is represented by
Ran\{f(x)\} = (-15, 12].

Explanation:

Let be
f(x) = -3\cdot x + 6, for
x \in [-2,7). As we notice that
f(x) 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 (
x = -2)


f(-2) = -3\cdot (-2)+6


f(-2) = 12

Upper bound (
x = 7)


f(7) = -3\cdot (7)+6


f(7) = -15

The range of the function is represented by
Ran\{f(x)\} = (-15, 12]

User Roldan
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