4Graphing Non Linear...
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4Graphing Non Linear Inequalities.notebook 1 October 01, 2013 WarmUp 1. If f(3) = 70, then f 1 (70) =? 2. What type of symmetry does y=x 2 2 have? 3. This function is even, finish the graph.
Transcript of 4Graphing Non Linear...
4Graphing Non Linear Inequalities.notebook
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October 01, 2013
WarmUp
1. If f(3) = 70, then f1(70) =?
2. What type of symmetry does y=x2 2 have?
3. This function is even,
finish the graph.
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Graphs of Nonlinear Inequalies
Chapter 3 Secon 3
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Graphing Nonlinear Inequalies
• Step 1: Determine solid line or dashed line
• Step 2: Graph the funcon using a solid line or dashed line
• Step 3: Determine shade above or below
• Step 4: Shade the appropriate region
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Solid/Dashed and Shading
• Solid lines: ≤ ≥
• Dashed Lines: < >
• Shade Above: > ≥
• Shade Below: < ≤
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Inequalies for Solid/Dashed and Shading
• < =
• > =
• ≤ =
• ≥ =
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Example
• Graph y < |x + 2| ‐ 3
> The graph should have a dashed line
> The graph y = |x| is shied 2 units to the le and 3 units down
> The region below the graph should be shaded
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Graphing Nonlinear Inequalies
• If you have the Inequalz App on your calculator, the program will do everything for you.
• If you do not have the program, your calculator can graph the funcon, you have to determine dashed or solid line and then shade above or below the graph
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Determining Soluons• Substute the x‐ and y‐values of the point
into the inequality and see if the statement is true
> If the statement is TRUE, it IS a possible soluon
> If the statement is FALSE, it is NOT a possible soluon
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Example• Determine if the points (0,6), (‐2,4), and (5,7) are soluons to the inequality y ≥ 2(x + 1)² ‐ 4
• (0,6) and (‐2,4) are soluons
6 ≥ 2(0 + 1)² ‐ 4
6 ≥ 2(1)² – 4
6 ≥ 2 – 4
6 ≥ ‐2 True
4 ≥ 2(‐2 + 1)² – 4
4 ≥ 2(‐1)² – 4
4 ≥ 2 – 4
4 ≥ ‐2 True
7 ≥ 2(5 + 1)² – 4
7 ≥ 2(6)² – 4
7 ≥ 72 – 4
7 ≥ 68 False
y x y x y x
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Solving Absolute Value Inequalies
• Step 1: Isolate the absolute value expression
• Step 2: Create 2 cases – Drop the absolute value bars and have one case as is and the other mulplied by ‐1
• Step 3: For the negave case, divide by ‐1, flip the sign
• Step 4: Isolate the variable for both cases
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Example• Solve |x + 3| ‐ 2 < 6
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Example 2• Solve |x – 4| + 5 < 9
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Example 2• Solve 2|x – 4| + 5 < 9
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Evaluation: Each worth 4 points
1. Which is the proper graph of
y > x4 2x3 + 2a b c d
2. What are the solutions to |2x3| ≤ 5
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Pracce• P. 150: 13, 14, 20‐24, 33‐35
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