Choose the table that represents g(x) = −2⋅f(x) when f(x) = x + 4.x g(x)1 −52 −63 −7x g(x)1 52 63 7x g(x)1 −102 −123 −14x g(x)1 −142 −163 −18
Accepted Solution
A:
Answer: THIRD OPTION.Step-by-step explanation: Since [tex]g(x) = -2f(x)[/tex], then [tex]g(x)[/tex] is: [tex]g(x)=-2( x + 4)\\\\g(x)=-2x-8[/tex] In order to find which table represents [tex]g(x) = -2f(x)[/tex] when [tex]f(x) = x + 4[/tex], you can follow these steps: 1. Substitute [tex]x=1[/tex] into the function [tex]g(x)=-2x-8[/tex]: [tex]g(1)=-2(1)-8\\\\g(1)=-10[/tex] 2. Substitute [tex]x=2[/tex] into the function [tex]g(x)=-2x-8[/tex]: [tex]g(2)=-2(2)-8\\\\g(2)=-12[/tex] 3. Substitute [tex]x=3[/tex] into the function [tex]g(x)=-2x-8[/tex]: [tex]g(3)=-2(3)-8\\\\g(3)=-14[/tex] Notice that those ouput values (for [tex]x=1,\ x=2[/tex] and [tex]x=3[/tex]) matches with the table provided in the third option. That table represents [tex]g(x) = -2f(x)[/tex] when [tex]f(x) = x + 4[/tex]: