Question

Question #c4eca

Answer 1

Your answer is given below:

Explanation:

As,`g(x)=|x|-2andf(x)=|x|`
So,`g(x)=f(x)-2`,it is the relation between`g(x)andf(x)color(blue)((Ans.))`
Again,`g(x)=|x-4|andf(x)=|x|`
Thus,`g(x)=|f(x)-4|color(red)((Ans.))`

Answer 2

See explanation.

Explanation:

`g(x)=|x|-2` vs. `f(x)=|x|`
The `-2` at the end of `g(x)` represents a vertical shift of 2 units down. Take the graph of `f(x)` and shift the whole thing down 2 units. This doesn't change the shape of the graph, just the location.

`g(x)=|x-4|` vs. `f(x)=|x|`
The `-4` inside the absolute value of `g(x)` represents a shift of 4 units to the right. Take the graph of `f(x)` and shift the whole thing 4 units to the right. Again, this doesn't change the shape, just changes the location.