1. Algebra 1
Section 5.5

2. The Function “Machine”
Values are chosen for x, put into the machine, manipulated by a function rule, and put out as corresponding y values.

3. Definition
A function rule is an equation that pairs each member of the domain with an element of the range.

4. Function Rule
If a function rule and the domain are given, then the entire function is defined and can be listed as a set, written as a table, graphed, or illustrated with a mapping diagram.

5. Example 1 Domain {-3, -1, 0, 2, 4}; f(x) = 3x + 2 x 3x + 2 f(x) -3 -12 4
3(-3) + 2 = -7
3(-1) + 2 = -1
3(0) + 2 = 2
3(2) + 2 = 8
3(4) + 2 = 14 -7 -1 2 8 14

6. Example 1 Domain {-3, -1, 0, 2, 4}; f(x) = 3x + 2

7. Example 2 Graph the function y = |x|. x |x| y -3 -1 2 52 5
f(-3) = |-3| = 3
f(-1) = |-1| = 1
f(0) = |0| = 0
f(2) = |2| = 2
f(5) = |5| = 5 3 1 2 5

8. Example 2
{(-3, 3), (-1, 1), (0, 0), (2, 2), (5, 5)} y x

9. Finding a Function Rule
You can often determine how a y-coordinate is related to its x- coordinate by examining a table of ordered pairs.

10. Example 3
As the values for x increase by 1, the values for y increase by 3.
Each y-value is 3 times the corresponding x-value.
f(x) = 3x

11. Example 6 Plan A costs $47/mo with unlimited minutes. A(m) = 47
Plan B costs $28/mo with a fee of $0.04/min.
B(m) = m

12. Example 6 Graph both functions on the same Cartesian plane.
Find the cost of 480 min for each plan and compare.
A(480) = 47
B(480) = (480) = 47.20

13. Example 6
A(480) = 47
B(480) = 47.20
Plan A is slightly less expensive for 480 min.

14. Example 6
From the graph, you can see that the two plans intersect at 475 minutes.
Plan A is less expensive if she talks more than 475 min/mo.
Plan B is less expensive if she talks less than 475 min/mo.

15. Homework: pp