Question

Domain and Range Find the domain and range of the function.

$f\left(x\right)=3x,-2\le x\le 6$

Short answer

The domain of the given function is $\left[-2,6\right]$and the range of the given function is $\left[-6,18\right]$.

Step-by-step solution

Step 1. Definition of domain and range.

The set of all input values of a function is known as the domain of the function.

The set of all output values of a function is known as the range of the function.

Step 2. Given information.

The given function is:

$f\left(x\right)=3x,-2\le x\le 6$

Step 3. Domain and range of the given function.

The given function is a linear function because it is in the form of $f\left(x\right)=mx+b$.

The given function is defined for $-2\le x\le 6$, so the domain is $\left[-2,6\right]$.

It is given that,

$-2\le x\le 6$

Multiply each side by width="10">3.

$\begin{array}{c}3\left(-2\right)\le 3x\le 3\left(6\right)\\ -6\le f\left(x\right)\le 18\end{array}$

Since $-6\le f\left(x\right)\le 18$, therefore the range is $\left[-6,18\right]$.

Thus, the domain of the given function is $\left[-2,6\right]$and the range of the given function is $\left[-6,18\right]$.