Question

How do you find the output of the function $y=3x-8$ if the input is $-2$?

Answer 1

We have been given the function $y=3x-8$ which we assume as $y=f\left( x \right)=3x-8$. Then the element of the domain $x=-2$ will be used in the function to find the output. We put the value $x=-2$ in the equation $f\left( x \right)=3x-8$ to find the solution.

Complete step-by-step answer:
We have to find the output of the function $y=3x-8$ if the input is $-2$.
We first assume the function as $y=f\left( x \right)=3x-8$.
The input $x=-2$ is an element of the domain of the function $f\left( x \right)=3x-8$. The output will be an element of the range equal to $f\left( -2 \right)$.
We have to put the value of $-2$ in the equation of $f\left( x \right)=3x-8$.
Therefore, $f\left( -2 \right)=3\times \left( -2 \right)-8$. We have to simplify the binary operation.
There is only one multiplication $3\times \left( -2 \right)=-\left( 3\times 2 \right)=-6$.
Then we have to complete the subtraction part and find the value where
$f\left( -2 \right)=-6-8=-14$.
Therefore, the output of the function $y=3x-8$ for the input of $-2$ is $-14$.

Note: We need to remember that the function has to be defined for the given value of $x=-2$. The function also has a domain A such that $2\in A$. Also, we have been given the function as y and variable as x, so students must never get confused and try to substitute y as -2 and end up finding the values of x.