Question

How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?

Answer 1

The lines have the same slope, so they'll be moving the same exact way except they have different y-intercepts.

Answer 2

The graph of g(x) is a translation of f(x) 2 units down.

Explanation:

Given : Graph of
`g(x)=3x-2` and
`f(x)=3x`

To find : How does the graph of g(x) compare to the graph of f(x)?

Solution :

`f(x)=3x`

`g(x)=3x-2`

We can re-write the g(x) as

`g(x)=f(x)-2`

The translation of a function is defined as

`g(x)=f(x)+b`

where, b is vertical shift.

If b>0, then f(x) shifts b units up and if b<0, then f(x) shifts b units down.

On comparing, b=-2<0.

So, the graph of f(x) shifts 2 units down.

The graph of g(x) is a translation of f(x) 2 units down.