Function Input and Output

1
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

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
• Substitute the input value for every instance of
  the independentvariable 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

• 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)
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) 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

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