ABSOLUTE VALUE ON GRAPHMATICA PLUS

You could have shifted up two first, then you could have Or f of x is equal to two times the absolute value And for x greater than negative three, it is going to look like. So let me see, I'm shifting it up by two. Here, in the orange function, whatever y value I gotДЇor the black function, I'm gonna have to get two more than that. Every point is going to shifted up by two or you can think about shifting Well whatever y value I was getting for this orange function, We're in the home stretch, I wanna graph, y is equal to two times the absolute value of Of x that we care about, we now need to add this two. So that is the graph of y is equal to two times the absolute And then instead of havingДЄ slope of negative one for values less than xД®quals negative three, I'm gonna have a slope of negative two. Of a slope of one, I'm gonna have a slope of two. So let me get my ruler out again and see if I can draw that. Than negative three, instead of having a slope of one, you're gonna have a slope of two. So what this is essentially going to do is multiple the slopes by a factor of two.

ABSOLUTE VALUE ON GRAPHMATICA PLUS

Now let's see if we can graph y is equal to two times theДЄbsolute value of x plus three. Little bit more intuitive sense of why if you replace x, if you replace x with x plus three, and this isn't just true ofДЄbsolute value functions, this is true of any function, if you replace x with x plus three, you are going to shift three to the left. Inside the absolute value sign at x equals zero. The absolute value sign, just as if you didn't shift it, you would have had zero And at x equals negative three, you have zero inside This upward sloping line right over here. Gonna get a positive value and so that's why you have Now for x is greater than negative three, when you add three to it, you're That's why you have thisДownward line right over here. Take it's opposite value and so that makes sense. Below x equals negative three, for x values less than negative three, what we're gonna have here, is this inside of the absolute value sign, is going to be negative and so then we're gonna Value sign is negative, we're gonna have a slope ofД®ssentially negative one. Value sign is positive, we're going to getД®ssentially, this slope of one. When whatever we have inside the absolute So if we shift three to the left, it's gonna look something like. And we're gonna do that right now and then we're gonna just gonnaД¬onfirm that it matches up. Subtracting from this x, that is how much you are shifting it. You could view this as the same thing as y is equal to the absolute If you replace your x, with an x plus three, this is going to shift your So the next thing I wanna graph, let's see if we can graph y.

And what they've already graphed for us, this right over here, this is the graph of y is equal To graph f of x is equal to two times the absolute value

Absolute value on graphmatica