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# Shifting absolute value graphs

The graph of y=|x-h|+k is the graph of y=|x| shifted h units to the right and k units up. See worked examples practicing this relationship.

## Want to join the conversation?

• I broke my replay button and I still don't understand this! Why move 3 to the right and write x-3 when x+3 seems to make sense?
• Because the part of "(x-3)", is the exact formula for it. even tho the number is actually "3", which is a positve, it has to be written as "x-3" because the "-" is mandatory, moving the number to the LEFT, this goes if the number is "x+3", therefore it will move to the RIGHT
• How the equation would be if we shift it only up 4?
• The answer would've been y=|x|+4
• Why would you subtract 3 if your are going to the right of the graph on the X-Axis instead of adding? So would that mean you would add if you were going the left of the X-Axis?
• I think you lack lifting y=x graph and need doing some practice or review.
When you subtract 3 you're shifting down 3 points on the Y-Axis
and
When you add 4 you're shifting up 4 points on the Y-Axis

OR

When you subtract 3 you're shifting right 3 points on the X-Axis
and
When you add 4 you're shifting left 4 points on the X-Axis
---
combining the both of point of views is NOT correct like you did:
When you subtract 3 you're shifting down 3 points on the Y-Axis
and
When you add 4 you're shifting left 4 points on the X-Axis
• Ummm... I think we use absolute value to find the distance from 0 to the number itself. Am I correct?
• Yes, you are correct. Absolute value finds the distance of a number from 0. For example, the absolute value of -3 is 3, but the absolute value of 99 is 99. Hope this helps!
(1 vote)
• wait.. so uhh can we like simplify
y = |x - 3| + 4
to
y = |x - 3 + 4|
and then simplify that to
y= |x + 1|
• Those are not the same equation.
y = |x-3|+4 has its vertex point at (3,4)
y = |x+1| has its vertex point at (-1,0)

Hope this helps.
• I am a bit confused (). What is Khan talking about when you switch signs? Why do you -3 to move it to the right? Is there is a way to explain this without using an example of plotting points?
• When he mentions switching signs he means what is inside of the abslute value signs. Let's first lok at just |x|.

|-1| = 1 and all other negative numbers are turned to positive. When you graph the absolute value function it makes a sudden sharp turn when you get to 0, which in other words is saying when you SWITCH SIGNS fro the negative numbers to non negative, the graph turns.

Why it moves 3 to the right is because you can move graphs around. You can move it up, down, left, and right. You just have to change the equation.

Specifically to move a graph to the right you need to determine the inside of the function. absolute value is pretty easy. inside the function is inside the absolute value bars. Once you find the inside of the function you just need to subtract a number from the variable to move right. so |x-1| goes to the right one. |x-2| goes tot he right two, and so on. if you add you go left, so |x+3| goes to the left 3.

If you are asking why it moves like that when you add or subtract then that is a little more tricky to answer. My suggestion is to think backwards with an answer and what youw ould need to change.

|x| has the angle at x=0. let's say we wanted it at 5 instead. We know we have to add or subtract something inside to make it happen. sothat means we will have x=5 and y = 0

|5+a|=0 So what does a have to be here? obviously -5 so that tells us |x-5| has the 0 point now at x=5, or in other words the graph was moved 5 places to the right.

Does that make sense?
• So is the white line always a V like that?
• In absolute value functions, the line it forms is always a V. It is not necessarily the same angle, and the vertex may be in a different spot, but it is a V nonetheless.
• I have no idea what this even means! From to the of the video, I don't understand anything stated in the video! How do you SWITCH signs in an absolute value? WHICH absolute value? And WHAT signs in an absolute value? An absolute value is just a number, what SIGNS are there to be switched?
• By switching signs, I think he means that the original function transforms some negative values of x (-3, -2, -1, etc...) into positive values of y (3, 2, 1, etc..) then, after x = 0, we're on the other side of the graph and it transforms positive values of x into positive values of y.

Yes, it's a bit difficult to visualize,
If you take the original function and look at the points you'll have:

x1 y1 To go from x1 to y1 you'll have to apply the absolute value each time
-3 3
-2 2
-1 1
0 0
1 1
2 2
3 3

If you shift the graph 3 units to the right, you'll have:

x2 y2 To go from x2 to y2, you need to substract 3, then apply the absolute value each time
0 3
1 2
2 1
3 0
4 1
5 2
6 3

Hope that helped?
Try similar tables with the shift up, see if you can make sense of this one too.
• What happens when you shift to the left?
(1 vote)
• Shifting three to the left would be the equation y = | x + 3 |