1. Warm Up 10/15/14
How much of a 25% solution would you need to mix with 20 ounces of a 46% solution to obtain a 32% solution?
If Jack can fetch a pail of water in 3 hours and Jill can fetch a pail of water in 4.5 hours, how long will it take them to fetch a pail of water together?

2. IF.1 Function Notation
There are many ways to show how pairs of quantities are related.
The relationships shown above all represent the same pairs of numbers.

3. IF.1 Function Notation
Domain: the input values of a quantitative relationship The domain of the table of values are those under the x The domain of the set of ordered pairs are the first numbers in the ordered pair The domain for the mapping diagram is the numbers are the left side

4. IF.1 Function Notation
Range: the output values of a quantitative relationship The range of the table of values are those under the y The range of the set of ordered pairs are the second numbers in the ordered pair The range for the mapping diagram is the numbers are the right side

5. IF.1 Function Notation
Mapping diagrams, ordered pairs, and tables are good to use when there are a limited number of input and output values. There are some instances when the domain has an infinite number of elements. In these cases it is better to use an algebraic rule or a graph to show the relationship. Often we will use equations as the algebraic rule for the relationships.

6. IF.1 Function Notation
Function: a quantitative relationship where each member of the domain is assigned to EXACTLY ONE member of the range. Are the examples from the beginning functions? Why or why not?

7. IF.1 Function Notation
Function Notation – Uses the notation f(x) (“f of x”), where f is the function and f(x) is the output of the function at the input x.

8. Examples
If , find f(-2).
For , find x if f(x) = -1

9. More Examples
f(-2) = If f(x) = -6, x =

10. Practice Problems
1. Find f(2) if 2. For , find x if f(x) = An athlete training for a marathon decides to start running 5 miles a day. Write a function, T, for amount of miles the athlete will run in d days.