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Nat2105 [25]
3 years ago
8

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 notat

ion.
Mathematics
1 answer:
Aliun [14]3 years ago
3 0

Answer:

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

Step-by-step 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]

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