2-7 Absolute Value Function Objective: I can write and graph an absolute value function

You jog at a constant speed. Your jogging route takes you across the county line. Suppose you graph your distance from the county line with respect to time. Sketch what you think the graph would look like?

Absolute Value Function f(x) = |x| xf(x)=|x| Domain: Range: All Real Numbers Vertex Axis of symmetry x = 0

Transformation of f(x) Translation: Vertical (k > 0) Translation: Horizontal (k > 0) Dilation: Vertical by a factor of a Reflection Up k units Down k units Right h units Left h units Stretch: Compression: Across x-axis Across y-axis N/A

Graphing Absolute Value Functions y = |x + 2| – 3 y = |x – 2| + 1 Vertex: (, ) – 2 – 3 Vertex: (, ) 21 Slope: a = Graph the vertex: (h, k) 2.Graph right branch: ±a factor is slope 3.Graph left branch: using symmetry

Graphing Absolute Value Functions y = 2|x| Vertex: (, ) 0 0 – 13 Slope: a = 2 1.Graph the vertex: (h, k) 2.Graph right branch: ±a factor is slope 3.Graph left branch: using symmetry

Writing an absolute value function from a graph 1.Identify the vertex (h, k) 2.Find the slope of the right branch, ±a Vertex: Slope: Vertex: Slope: Pg. 111 #10-28 evens 29, 30