[tex]\bf f(x)=x-1\qquad \qquad g(x)=3\cdot f(x)\implies g(x)=\underline{3(x-1)} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} x&g(x)\\ \cline{1-2} 1&0\\2&3\\3&6 \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6})[/tex]
[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{3-1}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=3(x-1)\implies y=\underline{3(x-1)}[/tex]
The table that represents g(x) = 3⋅f(x) when f(x) = x − 1 is that of Option D;
x g(x)
1 0
2 3
3 6
f(x) = x − 1
We want to find; g(x) = 3⋅f(x)
This means that; g(x) = 3(x - 1)
Looking at the options, the input values to be used are x = 1, 2 3.
When x = 1; g(x) = 3(1 - 1 )
g(x) = 0
When x = 2; g(x) = 3(2 - 1)
g(x) = 3
When x = 3; g(x) = 3(3 - 1)
g(x) = 6
Looking at the options, only the table in option D is correct.
Read more at; https://brainly.in/question/24797649
