2. Vocabulary A nonlinear function that can be written in the standard form Cubic Function 3.1Graph Cubic Functions A function where f (  x) =  f (x). The graph is symmetric about the origin. Odd Function A function where f (  x) = f (x). The graph is symmetric about the y-axis. Even Function The behavior of a function’s graph as x approaches positive infinity or negative infinity. End Behavior

3. Graph of the Parent Function For Absolute Value Functions 1.9Graph Absolute Value Functions Comparing Graphs of Absolute Value Functions with the Graph of f (x) = |x| The graph of g is a ___________ shift of the graph of f (x) = |x|. The shift is h units __________ if h > 0 and |h| units _______ if h < 0. The graph of h hh h (x) = |x + h| is a ______________ in the y-axis of the graph of g. horizontal right left reflection

4. Graph of the Parent Function For Absolute Value Functions 1.9Graph Absolute Value Functions Comparing Graphs of Absolute Value Functions with the Graph of f (x) = |x| The graph of g is a ___________ shift of the graph of f (x) = |x|. The shift is k units __________ if k > 0 and |k| units _______ if k < 0. vertical up down

5. Graph of the Parent Function For Absolute Value Functions 1.9Graph Absolute Value Functions Comparing Graphs of Absolute Value Functions with the Graph of f (x) = |x| If |a| > 1, the graph of g is a vertical _________ of the graph of f (x) = |x|. If 0 < |a| <1, the graph of g is a vertical ________ of the graph of (x) = |x|. The graph of h (x) = a |x | is a ____________ in the x-axis of the graph of g. stretch shrink reflection

6. 1.9Graph Absolute Value Functions Example 1 Compare the graph with the graph of f (x) = |x|. Make a table of values. Graph the function. Compare the graphs of g and f. x g(x)g(x) a. The graph of g(x) = |x + 1| is a ______________________________ of the graph of f (x) = |x|. horizontal shift 1 unit to the left

7. 1.9Graph Absolute Value Functions Example 1 Compare the graph with the graph of f (x) = |x|. Make a table of values. Graph the function. Compare the graphs of g and f. x g(x)g(x) b. The graph of g(x) = |x|  2 is a ___________________________ of the graph of f (x) = |x|. vertical shift 2 units down

8. 1.9Graph Absolute Value Functions The graph of g is a ___________________________ of the graph of f. horizontal shift 3 units to the right Checkpoint. Graph the function. Compare the graph with the graph of f (x) = |x|.

9. 1.9Graph Absolute Value Functions The graph of g is a ____________________ of the graph of f. vertical shift 2 units up Checkpoint. Graph the function. Compare the graph with the graph of f (x) = |x|.

10. 1.9Graph Absolute Value Functions Example 2 Compare the graph with the graph of f (x) = |x|. Make a table of values. Graph the function. Compare the graphs of g and f. x g(x)g(x) a. The graph of g(x) =  2 |x| opens ______ and is a ________________ of the graph of f (x) = |x|. down vertical stretch

11. 1.9Graph Absolute Value Functions Example 2 Compare the graph with the graph of f (x) = |x|. Make a table of values. Graph the function. Compare the graphs of g and f. x g(x)g(x) b. The graph of g(x) =  2 |x| opens ______ and is a ________________ of the graph of f (x) = |x|. up vertical shrink

12. 1.9Graph Absolute Value Functions Checkpoint. Graph the function. Compare the graph with the graph of f (x) = |x|. The graph of g opens up and is a vertical stretch of the graph of f.

13. 1.9Graph Absolute Value Functions Checkpoint. Graph the function. Compare the graph with the graph of f (x) = |x|. The graph of g opens down and is a vertical shrink of the graph of f.

14. 1.9Graph Absolute Value Functions