To translate an absolute value function left or right, you subtract a number from the variable inside the absolute value bars. The value of k is also the y-value of the vertex.Ībsolute Value Function with Vertical Translation We use the letter k to stand in for the vertical translation in our general equation. If the number you add is negative, then the graph will slide down. If the number you add is positive, the graph will slide up. To translate an absolute value function up or down, you add a number after the absolute value bars. We can translate our graphs vertically (up and down), horizontally (left and right), or both, through addition or subtraction. The values of h and k depend upon the translations performed on the original function.Ī translation is shifting a graph around the Cartesian Coordinate Plane. We have a general equation that describes the vertex as at the point ( h, k).
The point of the V is called the vertex of the function. The simplest absolute value function can be writtenĪnd can be read, “ y equals the absolute value of x.”Ībsolute value functions will graph in the shape of a V. When we evaluate absolute values, we simplify everything inside the absolute value bars, then we make the result a positive number. Taking the absolute value of a number or quantity is a mathematical function that describes how far the quantity is from zero on the number line. What should I know about functions involving absolute values, before I start working on a problem?
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