A2U1 Absolute Value Functions

An absolute value function is a function that outputs the distance of a number from zero on the number line, represented as f(x) = |x|.

The graph of y = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

The graph of y = |x + 2| + 2 moves left 2 units and up 2 units compared to y = |x|.

The vertex of the function f(x) = |x - 3| + 1 is (3, 1).

The new equation after translating is f(x) = |x + 1| - 3.

The slope of the function y = 2|x - 4| - 6 is 2, meaning it rises 2 units for every 1 unit it moves to the right.

An absolute value function opens upwards when the coefficient of the absolute value expression is positive.

A negative coefficient in front of an absolute value function causes the graph to open downwards.

The vertex is located at the point (h, k).

The function f(x) = |x - 4| + 3 is translated right 4 units and up 3 units from the parent function f(x) = |x|.