Question #c4eca

2 Answers
Dec 28, 2017

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.))#

Dec 28, 2017

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.