# How to graph transformations absolute value

## Absolute value graphs review

On to Piecewise Functions — you are ready! We actually could have done this in the other order, and it would have worked!

Share this page: An absolute value function is a function that contains an algebraic expression within absolute value symbols. Learn these rules, and practice, practice, practice! If you take x is equal to negative two, the absolute value of that is going to be two.

These two make sense, when you look at where the absolute value functions are. The less intuitive thing is what we did with x 'cause when you shift to the right, you actually replace your x with x minus the amount that you shifted but once again, try out numbers until it really makes some intuitive sense for you but this is what we would finally get.

## Absolute Value Functions

So at this point right over here, we know that our function, we know that our equation needs to evaluate out to zero and this is where it's going to switch signs and so we say, okay, well, this looks like an absolute value so it's going to have the form, y is equal to the absolute value of something and so you say, okay, if x is three, how do I make that equal to zero?

Also, if a is negative, then the graph opens downward, instead of upwards as usual. So let's just visualize what we're even talking about. So once again, I'm showing you this by really trying out numbers, trying to give you a little bit of an intuition because that wasn't obvious to me when I first learned this that if I'm shifting to the right which it looks like I'm increasing an x value but what I would really do is replace my x with an x minus the amount that I'm shifting to the right but I encourage you to try numbers and think about what's happening here.

Graphing absolute value functions. So whatever is inside the absolute value sign has to be equal to zero at x equals three and this, pause this video and really think about this if it isn't making sense and even as you get more and more familiar with this, I encourage you to try out the numbers. Current time: With this mixed transformation, we need to perform the inner absolute value first:. Follow us: If you're shifting in the vertical direction, if you shift up in the vertical direction, well, you just add a constant by the amount you're shifting.

So before, y equaled zero here but now, y needs to be equal to four. So whatever this was evaluating, do we now have to add four to it?

## Transformations of Absolute Value Functions

We're going up in the vertical direction. If you're seeing this message, it means we're having trouble loading external resources on our website.

It's when whatever was in the absolute value sign is switching from negative signs to positive signs. So that's what we first wanna figure out the equation for and so how would we think about it? Shifting absolute value graphs.

## Shifting absolute value graphs

Pretty crazy, huh? Let's see if it makes sense. So in particular, we're gonna first think about what would be the equation of this graph if we shift, if we shift three to the right and then think about how that will change if not only do we shift three to the right but we also shift four up, shift four up, and so once again pause this video like we always say and figure out what would the equation be if you shift three to the right and four up?