Function Input and Output Lesson 2.1

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

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

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)

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

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

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)

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

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

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

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