DO NOW

1) What is the graph of this inequality

-2y >= - 10 – 5x

2) M = 6 n = -34 ( m – 2) + 3n + 5Answers: 1) thru (0, 5) and shade right area2) 12

Think…..: )

• How do variables help you model real world situations?

• Can we say variables are x, y and also independent and dependent?

Domain, Range, restrictions

Unit 1 modeling functions

Review: Graphing Points

Graph points:A(-4, 2)B(3, 1)C(0, -3)D(-2, 0)

Argumentation

• Based on the results of the Absolute Value Discovery, attempt similar transformations for either the quadratic function f(x) = x^2, the cubic function f(x) = x^3, or the exponential function f(x) = 2^x.

• Analyze and explain the rationale for why the transformations apply to this (and other) functions

Vocabulary

Domain – independent variable, x value, More than one input that that can leadTo the same output as another domain

Range – dependent variable, y value, Exactly one range leads back to one or more domain, the output

x represents _________________

y represents _________________

The summer before going to college, a student earned a promotion to shift supervisor at her job at Starbucks! The new position pays $10.20/hour.If the student's paycheck was modeled by a function, what would be the domain and range? Explain your answer. Why is this domain and range different than other similar functions?

Answers:

X = hoursY = paycheck amount

Domain and range notes

• 1) Dustin charges $10 per hour for mowing lawns. What is the function

• D(h) = 10 h, h >= 0 (because cannot work negative hours)

• Domain: non neg rational #s• Range: non-neg rational #s

• 2) maria charges $25/hour for tutoring math, with a minimum charge of $15

M(h) = $15 0 <= 0 <= 3/5 hours (15/25) $25 h h > 3/5hours

Domain: non neg rational #sRange: rational #s >= $15

Domain and range notes

Domain and range

• F(X) = 2x^2 + 5

• D: all real #s (the 2x^2 makes this non neg)• R: all real #s >= 5 (since y intercept is 5)

Domain and range

• F(x) = 15 x – 12

• Domain: all real numbers• Range: all real numbers

Assessment prompt #2(independent) What are the domain and range of:

f(x) = x f(x) = x

f(x) = x f(x) = 2

f(x) = x f(x) =

Are there any restrictions?

Create graphs of functions with the following domains:{All real numbers}, {All real numbers for x 0}, {All real numbers for x 0), {All real numbers for x < 0}, {All positive integers}, and {All integers}.

1.How do your graphs accurately represent the required domains?

2. What are the similarities and differences between your graphs? 3. For each graph, think of either a math function OR a real-world situation where the domain would apply. Explain why your math function OR real-world situation must have the domain you identified.

Argumentation

Still to come

• Rate of change• Patterns in graphs• Literal equations• Square root functions

You do

• Pg. 73• #s 62, 63, 64• Graph each relation and find the domain and

range.• Do on loose notebook paper, you will turn in

today

summary

• Why do functions have restrictions? Explain how you would know.

• Answer in notebook

homework

• On homework chronicle• Did you turn in today’s homework?