Question

Graph g(x), where f(x) = 3x − 1 and g(x) = f(x + 1).

a line labeled g of x that passes through points negative 2, negative 4 and 0, 2
a line labeled g of x that passes through points 0, negative 4 and 2, 2
a line labeled g of x that passes through points negative 1, negative 3 and 0, 0
a line labeled g of x that passes through points 0, negative 2 and 2, 4

Answer 1

a line labeled g of x that passes through points negative 2, negative 4 and 0, 2

`\huge \mathfrak{Explanation}\\</p><p>g(x)=f(x+1)=3(x+1)-1\\</p><p>g(x)=3x+2`

A line y=g(x) is y=3x+2.

1)Put x=-2

`\implies g(-2)=3(-2)+2=-6+2=\color{red}{-4}`

2)Put x=0

`\implies g(0)=3(0)+2=\color{red} {2}`

Answer 2

It's a line labeled
`g(x)` that passes through points
`(-2;-4)` and
`(0;2)`,

Explanation:

To graph
`g(x)`, first we have to find that function by replacing
`f(x)`.

The
`g(x)` is defined as the first function but with its variable increased by 1 unit, instead of
`x`, we write
`x+1` as its variable.

`g(x)=f(x+1)=3(x+1)-1`

`g(x)=3x+3-1`

`g(x)=3x+2`

So, if we graph this function we'll have something like the image attached. It's a line labeled
`g(x)` that passes through points
`(-2;-4)` and
`(0;2)`, which is showed on the graph.