Question

How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?

1.The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units.

2. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.

3. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units.

4. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.

Answer 1

The answer is the option
`4`

The graph of
`g\left(x\right)=\left|x\right|-3` is the graph of
`f\left(x\right)=\left|x\right|` shifted down
`3` units

Explanation:

we have

`f\left(x\right)=\left|x\right|`

The vertex of the function f(x) is the point
`(0,0)`

`g\left(x\right)=\left|x\right|-3`

The vertex of the function g(x) is the point
`(0,-3)`

therefore

The rule of the translation of f(x) to g(x) is equal to

`(x,y)-------> (x,y-3)`

That means-------> The translation is
`3` units down

Answer 2

4. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.

Explanation:

The -3 is a shift of 3 units down.

Answer:

4. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.