2.5 – Absolute Value Graphs and Tranlsations

I. Graphing Absolute Value Functions  Vertex – where direction changes

 Example 1: Describe the domain and range of any absolute value graph.  1A) Apply to this graph: f(x) = │ x - 3 │ + 2

II. Translating Absolute Value Graphs  When translating any functional graph, we can identify a parent function.  Parent function: the most basic form f(x) = │ x │

 The form of absolute value after translations is: f(x) = a │ x - h │ + k a = the scalor (wide versus skinny) h = horizontal slide (notice sign is opposite) k = vertical slide (sign is the same)

 Example 2: Describe the position of the graph. (which quadrant with no calculators!) A)f(x) = - │ x + 4 │ - 3 B)g(x) = -.5 │ x │ + 14 C)h(x) = 10 │ x - 4 │ + 1

 Example 3: write the equations of the given graphs, with the domain and range.