y x Lesson 3.7 Objective: Graphing Absolute Value Functions. EQ: How do you transform an absolute value function? Solve & Graph #1: y = |x| Step 1 – create a table x y Step 2 – plot the ordered pairs Step 3 – draw the V-shaped graph x y Domain: All Real Numbers Range: Y ≥ 0

A basic function used as building blocks for more complicated functions. Parent function: Absolute value function: A function that contains an absolute value equation. The Parent function for an absolute value function is y=|x| Vertex: The point where the graph changes direction. The VERTEX of the parent absolute value function y= |x| is (0,0) or the origin. Translating graphs: The rigid movement of a function vertically or horizontally.

y x y x g(x) = |x – 2| The graph translated 2 units to the right x g(x) -5 -3 -1 1 2 3 7 5 3 2 1 1 How did this function change? x y g(x) = |x + 2| The graph translated 2 units to the left x g(x) -3 -2 -1 1 2 3 1 1 2 3 4 5 How did this function change?

y x y x f(x) = | x | - 2 x The graph translated 2 units down f(x) f(x) -3 -2 -1 1 2 3 1 -1 -2 -1 1 How did this function change? x y The graph translated 2 units up f(x) = | x | + 2 x f(x) -3 -2 -1 1 2 3 5 4 3 2 3 4 5 How did this function change?

y x y x The graph narrowed / stretched g(x) = 2 | x | x g(x) g(x) -3 -2 -1 1 2 3 6 4 2 2 4 6 How did this function change? Vertical Stretch. By a factor of 2 x y g(x) = ½ | x | The graph grew wider / shrank x g(x) -4 -2 -1 1 2 4 2 1 .5 .5 1 2 How did this function change? Vertical Shrink. By a factor of ½

y x x f(x) = - | x | f(x) How did this function change? f(x) -3 -2 -1 1 2 3 -3 -2 -1 -1 -2 -3 How did this function change? The graph reflected over the x-axis

y x y x f(x) = |2 x | x f(x) How did this function change? x f(x) -3 -2 -1 1 2 3 6 4 2 2 4 6 How did this function change? Horizontal shrink by factor of ½. f(x) = | ½ x | x y x f(x) -4 -2 -1 1 2 4 2 1 .5 .5 1 2 How did this function change? Horizontal stretch by a factor of 2