Respuesta :
The function we have is:
[tex]y=3x+5[/tex]We are given the domain of the function:
[tex]D=(-4,-1,2,5)[/tex]The domain of a function is the allowed values for x.
And we are asked to find the range, which is the values that the function returns for the x-values of the domain.
To find the range, we need to take the values of the domain, substitute them into the equation, and find the values that the function returns.
For the given domain, the allowed values for x are:
[tex]\begin{gathered} x=-4 \\ x=-1 \\ x=2 \\ x=5 \end{gathered}[/tex]For x=-4
We substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(-4)+5 \end{gathered}[/tex]And solve to find the first value of the range:
[tex]\begin{gathered} y=-12+5 \\ y=-7 \end{gathered}[/tex]For x=-1
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(-1)+5 \end{gathered}[/tex]Solve the operations:
[tex]\begin{gathered} y=-3+5 \\ y=2 \end{gathered}[/tex]For x=2
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(2)+5 \end{gathered}[/tex]And again, solve the operations:
[tex]\begin{gathered} y=6+5 \\ y=11 \end{gathered}[/tex]For x=5
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(5)+5 \end{gathered}[/tex]Solve the operations:
[tex]\begin{gathered} y=15+5 \\ y=20 \end{gathered}[/tex]The values we have found for y are the range of the function:
[tex]R=(-7,2,11,20)[/tex]Answer:
The range of the function is (-7,2,11,20)
