Answer:
a line labeled g of x that passes through points negative 2, negative 4 and 0, 2
[tex] \huge \mathfrak{Explanation}\\
g(x)=f(x+1)=3(x+1)-1\\
g(x)=3x+2[/tex]
A line y=g(x) is y=3x+2.
1)Put x=-2
[tex]\implies g(-2)=3(-2)+2=-6+2=\color{red}{-4}[/tex]
2)Put x=0
[tex]\implies g(0)=3(0)+2=\color{red} {2}[/tex]
Answer:
It's a line labeled [tex]g(x)[/tex] that passes through points [tex](-2;-4)[/tex] and [tex](0;2)[/tex],
Step-by-step explanation:
To graph [tex]g(x)[/tex], first we have to find that function by replacing [tex]f(x)[/tex].
The [tex]g(x)[/tex] is defined as the first function but with its variable increased by 1 unit, instead of [tex]x[/tex], we write [tex]x+1[/tex] as its variable.
[tex]g(x)=f(x+1)=3(x+1)-1[/tex]
[tex]g(x)=3x+3-1[/tex]
[tex]g(x)=3x+2[/tex]
So, if we graph this function we'll have something like the image attached. It's a line labeled [tex]g(x)[/tex] that passes through points [tex](-2;-4)[/tex] and [tex](0;2)[/tex], which is showed on the graph.
