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Function Input and Output Lesson 2.1

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2 The Magic Box Consider a box that receives numbers in the top And alters them somehow and sends a (usually) different number out the spout For each of the number combinations, can you figure out the "rule" which alters the number? 1 -3 4 3 3 1 Today we look at the mathematical way of talking about the "rule"

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3 The Magic Box Consider a box that receives numbers in the top And alters them somehow and sends a (usually) different number out the spout

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4 Output Values Output Value Evaluating the Function Substitute the input value for every instance of the independent variable in the function Input Value Output value f(x)

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5 Evaluating a Function Given Determine the value of the function h when x = 2 h(2) = ? Determine h(-4)

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6 Evaluating a Function Calculator can evaluate functions Also possible to evaluate for symbolic values of the independent variable

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7 Finding Input Values Consider the function as a box with a funnel and spout … What if we knew what was coming out and wished to know what went in that gave that result Independent Variable Dependent variable h(x)

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8 Finding Input Values Try using the “solve ( )” command on your calculator Press Diamond, Enter to force decimal answer

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9 Finding Input Values Given g(x) = x 2 – 2x + 4 g(x) = 12 x = ? Create an equation using the formula and the output 12 = x 2 – 2x + 4 Solve for all possible values of x which make that statement true

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10 Possible Solution Strategies Algebraic –factor the quadratics Look at tables of values Graph the function –create a horizontal line (i.e. at y = 4.4) –note the intersection Use the solve command on the calculator

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11 For You to Try Try together in class on page 64 –Ex 8, 9 Assignment –Page 66 –Exercises 3, 5, 10, 13, 15, 19, 25, 29, 31, 35, 37

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Lesson 9.7 Solve Systems with Quadratic Equations

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