Transcript What are the domain and range of

DO NOW
1) What is the graph of this inequality
-2y >= - 10 – 5x
2) M = 6
n = -3
4 ( m – 2) + 3n + 5
Answers: 1) thru (0, 5) and shade right area
2) 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 lead
To the same output as another domain
Range – dependent variable, y value,
Exactly one range leads back to one or
more domain, the output
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?
x represents _________________
Answers:
y represents _________________
X = hours
Y=
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
Domain and range notes
• 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 #s
Range: rational #s >= $15
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?
Argumentation
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.
Still to come
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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?