1. Function Input and Output
Lesson 2.1

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

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
Input Value
Output value
Output Value Evaluating the Function
Substitute the input value for every instance of the independent variable in the function
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
Independent Variable
Dependent variable
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
h(x)

8. Press Diamond, Enter to force decimal answer
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) = x2 – 2x + 4 g(x) = 12 x = ?
Create an equation using the formula and the output = x2 – 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 Assignment Ex 8, 9
Exercises 3, 5, 10, 13, 15, 19, 25, 29, 31, 35, 37