gr 10 absolute value functions and graphs
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2-5 Absolute Value Functions and Graphs
cbmxy
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xxf )(
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Vertex
• Maximum or minimum of the graph
• For the equation, the vertex is at
c
m
b,
cbmxy
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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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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 |
0 3
1 2
2 1
3 0
4 1
5 2
x | x + 2 |
–4 2
–3 1
–2 0
–1 1
0 2
1 3
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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.
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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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The recommended dietary allowancefor vitamin C is 2 micrograms per day.Write an absolute value function for the differenceBetween the number of micrograms of Vit C you atetoday x and the recommended amount.
X Y
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Graph
342
3 xy
X Y
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Graph
• y = | -x – 5 |
X Y
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Graph
• y = | -3x |
X Y