When graphing the any absolute value function, it's important to know the graph of the parent function f(x) = |x|. This looks like a v with the vertex at the origin and slope of -1 from -infinity to 0, and slope of 1 from 0 to infinity.

From here we can graph any of them in this form a|x +/- h| +/- k

If a is positive, the shape is a v, if it's negative it's an upside down v and the value of a determines the slope.

If it's x + h, the graph shifts h units to the left and if it's x - h, it shifts h units to the right.

If it's + k, it shifts k units up and if it's -k, it shifts k units down. The point we are shifting is the vertex.

For example,

f(x) = 4|x + 3| - 2, the vertex moves 3 to the left and 2 down to (3, -2) and the slope is 4 from 0 to infinity and -4 from -infinity to 0.

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