When you have the graph y = f(x)... (10 points)?

Question

What is the difference in the graphs between y = f(|x + 2|) and y = f(|x| + 2)??

Also, how does y = - |f(2 - x)| affect the graph of y = f(x)?

Thanks.

Answer 1

The difference is in the negative scale. Because mathematically, both equations are the same if X>0.

Consider that x=-10.

For y1=f(|x+2|):

y1=|(-10)+2)|

y1=|-8|

y1=8

For y2=f(|x|+2):

y2=|(-10)|+2

y2=10+2

y2=12

Now consider x=-20

For y1=f(|x+2|):

y1=|(-20)+2)|

y1=|-18|

y1=18

For y2=f(|x|+2):

y2=|(-20)|+2

y2=20+2

y2=22

Answer 2

|x+2| ≠ |x|+2, which you can prove by testing x = -2:

|x+2| = |-2+2|

= |0|

= 0

|x|+2 = |-2|+2

= 2+2

= 4