Function input and output
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Function Input and Output. Lesson 2.1. 1. 4. 3. -3. 3. 1. 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. Today we look at the mathematical way of talking about the "rule".

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The magic box l.jpg

1

4

3

-3

3

1

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

Today we look at the mathematical way of talking about the "rule"

For each of the number combinations, can you figure out the "rule" which alters the number?


The magic box3 l.jpg
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


Output values l.jpg

Input Value

Output value

Output Values

  • Output Value Evaluating the Function

  • Substitute the input value for every instance of the independentvariable in the function

f(x)


Evaluating a function l.jpg
Evaluating a Function

  • Given

  • Determine the value of the function h when x = 2 h(2) = ?

  • Determine h(-4)


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Evaluating a Function

  • Calculator can evaluate functions

  • Also possible to evaluate for symbolic values of the independent variable


Finding input values l.jpg

Independent Variable

Dependent variable

Finding Input Values

  • Consider the function as a box with a funneland spout …

  • What if we knew what was comingout and wished to know what went in that gave that result

h(x)


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Finding Input Values

  • Try using the “solve ( )” command on your calculator

Press Diamond,Enter to force decimal answer


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Finding Input Values

  • Given g(x) = x2 – 2x + 4 g(x) = 12 x = ?

  • Create an equation using the formula and the output 12 = x2 – 2x + 4

  • Solve for all possible values of x which make that statement true


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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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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