Question

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.

Answer 1

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 $Ran\{f(x)\} = (-15, 12]$