Question

could someone please explain the difference between f (|x|) and |f(x)| in how it relates to graphs?

Answer 1

f(|x|) applies the absolute value to each x value while |f(x)| applies the absolute value to the final result


For instance, if f(x)=2x^2+3x+5, then f(|x|) = 2|x|^2+3|x|+5 and |f(x)| = |2x^2+3x+5|


The first will be a graph that is symmetric by the y-axis while the second will always be positive (ie so the graph of |f(x)| will NOT lie in quadrants III or IV)

Answer 2

so would both graphs be symmetric to the y-axis?

Answer 3

f(|x| ) always is, but |f(x) | may not be all the time

Answer 4

for
\[f(|x|) \]forget what you see to the left of the y - axis . it will be the mirror image of the right.
here is an example with
\[f(x)=x^3-3x^2-18x+9\]
http://www.wolframalpha.com/input/?i=y%3Dx^3-3x^2-18x%2B9
versus
\[f(|x|)\]
http://www.wolframalpha.com/input/?i=y%3D |x|^3-3|x|^2-18|x|%2B9

Answer 5

and here is
\[|f(x)|\]
http://www.wolframalpha.com/input/?i=y%3D |x^3-3x^2-18x%2B9|

Answer 6

copy and paste whole link . you will see that
\[|f(x)|\] reflects what is below the y-axis to above

Answer 7

http://www.wolframalpha.com/input/?i=y%3D |x^3-3x^2-18x%2B9|

Answer 8

nope still didn't work. copy and paste

Answer 9

i got the image of the first one but i cant get the image of |f(x)|

Answer 10

for some reason the absolute values signs make it hard to copy. open wolfram and type in

y=|x^3-3x^2-18x+9|

you will get it

Answer 11

thanks!

Answer 12

copying and pasting link works too, you just can't click on it

Answer 13

just got it!