Question

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to graph the given function.

Answer 1

\[h(x) = 2| x | + 2 \]

Answer 2

@Psymon can you help?

Answer 3

Well, do you know what theoriginal |x| graph looks like?

Answer 4

no!

Answer 5

Yeah, that's the important part. With these transformations, they expect you to know what the beginning graph looks like. If you don't know what |x} looks like then there is no quick way to do this problem. Well, the |x| graph looks like this:



The beginning graph should be symmetric about the y-axis. We have (1,1) (2,2), (3,3) etc and then the same thing on the opposite side (-1,1), (-2,2), (-3,3) etc.

Answer 6

So we have several transformations that can occur. We can have horizontal and vertical shifts and we can have horizontal and vertical stretching and shrinking. The function tells us which kind of transformation we use depending on what the function looks like. Make sense so far?

Answer 7

yes it does.

Answer 8

Alright, so I'll start with horizontal shifts since I think that's the best one to start with. So we have several grouping symbols we use parenthesis and brackets ( ) [ ], radicals like √ and absolute value bars like | |. Now these are important because horizontal shifts occur only when we have numbers inside of these grouping symbols. Now your problem does not have this, but I still think it's good to point out. So if we ever have a +/- a number being applied to x INSIDE a grouping symbol, we move the graph leftor right from the starting point. A negative number, like |x-2| means we go right that many units. A positive number |x+2| means we go left that many units. Now this only occurs when we are inside of grouping symbols. When +/- numbers are NOT inside of grouping symbols we have a shiftup and down. Your function has a + 2 that is not paired with x inside of a grouping symbol, so this means we just move our starting graph up 2. So moving our graph up 2 we get this:



Read that over and see if you get what I mean with horizontal and vertical shifts.