Transcript Evaluating Functions

Function Input and Output
Lesson 2.1
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
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Today we look at the
For each of the number
mathematical
way of
combinations, can you figure
talking
about
the
out the "rule" which alters the
"rule"
number?
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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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Output Values
Input Value
Output Value
Evaluating the Function
f(x)
Substitute the input value for
every instance of the independent
variable in the function
Output value
x 5
h( x )  2
x 1
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Evaluating a Function
Given
x 5
h( x )  2
x 1
Determine the value of the function h
when x = 2 h(2) = ?
2  5 3
h(2) 
Determine h(-4)
2 1
2

3
 1
4  5
9
h(4) 

2
(4)  1 15
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Evaluating a Function
Calculator can evaluate functions
Also possible to evaluate for symbolic
values of the independent variable
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Finding Input Values
Independent Variable
Consider the function
as a box with a funnel
and spout …
x 5
h( x )  2
x 1
h(x)
Dependent variable
What if we knew what was coming
out and wished to know what went in that
gave that result
h( x)  3
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 0  x 2  2 x  8
0  ( x  4)  ( x  2)
x  4 or x  2
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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
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