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2-5 Absolute Value Functions and Graphs
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Vertex Maximum or minimum of the graph
For the equation, the vertex is at
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Identify the vertex for each function
1. f(x) = | 2x – 5 | 2. f(x) = | 3x + 6 | 3. f(x) = - |x + 1 | - 2
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Graphing absolute value functions by making a table
Find the vertex Make a table of values (at least 5!) Graph the function.
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Find several ordered pairs for each function.
Graph and on the same coordinate plane. Determine the similarities and differences in the two graphs. Find several ordered pairs for each function. x | x – 3 | 3 1 2 4 5 x | x + 2 | –4 2 –3 1 –2 –1 3 Example 6-3a
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Graph the points and connect them.
Answer: The domain of both graphs is all real numbers. The range of both graphs is The graphs have the same shape, but different x-intercepts. The graph of g (x) is the graph of f (x) translated left 5 units. Example 6-3b
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Graph y = | x – 3 | + 3 X Y
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Graph y = | 2x + 1 | X Y
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X Y The recommended dietary allowance
for vitamin C is 2 micrograms per day. Write an absolute value function for the difference Between the number of micrograms of Vit C you ate today x and the recommended amount. X Y
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Graph X Y
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Graph y = | -x – 5 | X Y
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Graph y = | -3x | X Y
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