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 To actually put numbers onto this, you would lookk at your equation to get the vertex of the function (6, -10) and use the positive and negative slope to draw the two parts of the function. So our correct graph should be less steep than a normal absolute value function, and translated down and to the right. Since we have a low (<1) coefficient inside the function, the graph will horizontally get squished, or vertically stretch. While a high coefficient on the outside would increase every y-value by a certain factor (vertically stretch the graph), a high coefficient on the inside would increase every x-value by a certtain factor (horizontally stretch, which makes the graph wider). Now that the equation has been simplified to y = |1/2 (x - 6)| - 10, you can get to graphing.įor any function, if you have a coefficient inside the operation of the function (the absolute value bars in this case), it basically does the opposite of a coefficient on the outside. Because absolute value doesn't care about the sign, you can effectively just remove the negative on the 1/2.

Now you're taking the absolute value of something (x - 6) times a negative. If you do that to this problem, you'll get this: If you have a coefficient of x inside the absolute value sign, one thing you can do is try and isolate it a little bit, by setting it as a factor to the rest of the inside of the absolute value. I'll assume you're asking how to graph the equation.

Khan academy absolute value equations