The Solution:
The given function is
[tex]g(x)=-4x-1[/tex]The given table is found below:
To find A, that is, the value of g(x) when x =7.
we shall substitute 7 for x in g(x) as below:
[tex]\begin{gathered} g(7)=-4(7)-1=-28-1=-29 \\ A=g(7)=-29 \end{gathered}[/tex]To find x when g(x) = 0, we shall substitute 0 for g(x) as below:
[tex]\begin{gathered} 0=-4x-1 \\ 1=-4x \\ -4x=1 \\ \text{Dividing both sides by -4, we get} \\ \frac{-4x}{-4}=\frac{1}{-4} \\ \\ x=-\frac{1}{4} \\ So, \\ B=-\frac{1}{4} \end{gathered}[/tex]To find g(x) when x = -13, we shall substitute -13 for x as below:
[tex]\begin{gathered} g(-13)=-4(-13)-1=52-1=51 \\ So,\text{ } \\ C=51 \end{gathered}[/tex]