Can I treat absolute value functions as separate functions for graphing?

[Dell]

when i am exploring a function eg. f(x)=|2x-6|

can i treat it as two separate function all the way through, one to the left of x=3 and one to the right, and only at the very end, when i draw the graph connect them, ie draw a graph according to all the values i found from each side? will this work whenever i have absolute value of a basic polynom, should this always come out as a mirror image?

 

[Mark44]

when i am exploring a function eg. f(x)=|2x-6|

can i treat it as two separate function all the way through, one to the left of x=3 and one to the right, and only at the very end, when i draw the graph connect them, ie draw a graph according to all the values i found from each side?

Yes. You won't have to connect them at the end, since the two halves will already be connected at x = 3.

will this work whenever i have absolute value of a basic polynom, should this always come out as a mirror image?

Yes, if you mean the mirror image across the x-axis. Take for example the function g(x) = |x^2 - 2x|. For x < 0 or x > 2, the graph looks exactly like that of the parabola y = x^2 - 2x. However, for 0 < x < 2, the portion of the graph of the parabola that lies below the x-axis is relected across it.