Graphing absolute value

[jinx24]

I have several homework questions like this one and I just wanted to make sure I am on the right track. I am pretty sure I am doing these right, but the absolute value is making me second guess myself.

"Sketch the graph of the function, y = -f(x - 5), given that f is defined as follows:
f(x) = |x| "

f(x) = -|x - 5|

So, this is what I came up with:

y = |x| Basic

y = -|x| Reflection about the x-axis

y = |x - 5| Horizontal Shift to the right 5 units ??

y = -|x - 5| No Y-axis Reflection...Final graph

My only question is regarding the horizontal shift. Is it to the right because it is -5 or to the left because it is in the absolute value and the absolute value of -5 is +5?

Thank you.
Jenny

 

[tkhunny]

I like to think about behavior, rather than memorizing directions.

f(x) = |x| -- What is its behavior around x = 0?

g(x) = |x-5| -- Where does this exhibit the same behavior? x-5 = 0, x = 5.

Did it shift right or left?

 

[jinx24]

I don't really know what you mean by behavior, but I'll give a shot anyway.

f(x) = |x| Its "behavior" around x = 0 is the vertex.

g(x) = |x-5| Where does it have the same behavior? x-5 = 0, x = 5

So the graph would shift, and the new vertex would be at x = 5; the graph shifted to the right.

 

[tkhunny]

I think you have it.

"Behavior" is not a technical term. Just look at the graph. If there were some part of it that is more interesting than the rest of it, what part would that be? Whatever that part is might be called "interesting" behavior. Everywhere else it just sort of sits around.