1. Functions and Systems of Equations
Function Notation
Systems of Linear Equations
Solving using the Substitution Method
Solving using the Elimination Method

2. Total Revenue for GE Find an equation for a model of these data.
b) Using your model, estimate GE’s revenue in 2010
c)What is the slope of your model?
What does it mean in regard to GE’s revenue

3. Relation = set of ordered pairs.
Relation between elements of a set of input and elements of a set of outputs
(4,11)
x + 2y = 12

4. Function = every input there is only one output
For each input value in the domain, you must have one and only one output value in the range.
{(1,2) , (3,4) , (5, 6) , (7,8)} 1 4 5 7 9 3 4 5 6 9

5. Function or Not? The Set A = {(2,5), (4,8), ( 10,8), (20,15)} 90 88 91
Day of Week
Monday
Wednesday
Saturday
Temperature
(degrees Fahrenheit) 90 88 91 93

6. Vertical Line Test
Given the graph of an equation utilize a vertical line. Try to determine how many times the vertical line touches the equation. Vertical Line Test = any vertical line intersects a graph in at most one point, the graph represents a function

7. Function or Not?
𝑦=7𝑥 −20 𝑦 2 = 4𝑥 2 +16

8. Notation
f(x)
“f of x”
Represents a function named f that depends on the variable x
f means output/y-variable/range
Shorthand method of providing information in a compact form.

9. Example
𝑃(𝑡) = population of Hawaii (in milliions) 𝑡 = Years since 2000 Then the population of Hawaii at time t can be represented by the following function. 𝑃 𝑡 =0.013𝑡+1.21

10. Word problems and Function Notation
𝐻(𝑡) = height of a toy rocket in feet t seconds after launch.
What does 𝐻(3) = 12 mean?
𝐶(𝑚) = Cost in hundred of dollars for producing m miracle mops.
𝐶 (2500) = 189
𝑃(𝑡) = population of Michigan, in millions, t, years since 2000.
𝑃(10) = 10.4

11. Writing models in Function notation
Define the variable
Create Scatterplot
Choose model type{linear, quadratic, poly….)
Linear: Determine the slope and y-int
Check model by graphing.

12. Population of Wisconsin, in millions
Find an equation for a model of these data. Write your model in function notation.
Determine a reasonable domain and range
Find P(14) and interpret its meaning in regard to the pop of Wisconsin.

13. Using Function Notation
𝑓 𝑥 =7𝑥+2 𝑔 𝑥 =−1.25𝑥+14 ℎ 𝑥 =2 𝑥 2 −10 Find: 𝑓 3 ℎ 5 𝑔 𝑥 =15

14. Domain and Range
In an application need to consider model breakdown. In an equation Domain: set of all real numbers that make the function defined. (Division by zero and imaginary numbers need to be avoided) Range: set of all possible output values resulting from values of the domain.

15. Systems of Linear Equations
Set of two or more linear equation Solution: An ordered pair (or set) that is a solution to every equation in the system.