Vocabulary The distance to 0 on the number line. Absolute value 1.9Graph Absolute Value Functions Transformations of the parent function f (x) = |x|.

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Vocabulary The distance to 0 on the number line. Absolute value 1.9Graph Absolute Value Functions Transformations of the parent function f (x) = |x|. Absolute value Function

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

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

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

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

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

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|.

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|.

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

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

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.

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.

1.9Graph Absolute Value Functions