today in calculus… warm up: linear equations multiple choice learning targets : you will be...
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TODAY IN CALCULUS…
WARM UP: Linear Equations multiple choice
Learning Targets : You will be able to identify the domain and range
of a function using its graph or equation. You will be able to recognize even functions and
odd functions using equations and graphs. You will be able to interpret and find formulas for
piecewise defined functions.
Independent practice
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WARM UP: 1. Which of the following is an equation of the line through with
slope ?a) b) c) d)
2. Which of the following is an equation of the vertical line through ?
a) b) c) d)
3. Which of the following is the x-intercept of the line ?
a) b) c) d)
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1.2 FUNCTIONS
Function Machine
input
output
𝒙
𝒚
DOMAIN
RANGE
Independent variable
Dependent variable
FUNCTION: a relationship between two variables such that each independent value corresponds to exactly one dependent value• No repeated x values• Exactly one input paired with
one output• Domain: independent values• Range: dependent values
FUNCTION NOTATION: • y is a function of x.• y is dependent on x.
EXAMPLE: • P is a function of t.• P is dependent on t.
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1.2 FUNCTIONSEXAMPLE: Which of the equations below define y as a function of x?a. b.
c. c.
FUNCTIONNOT A FUNCTION
NOT A FUNCTIONFUNCTION
X Y
X Y
X Y
X Y
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1.2 FUNCTIONSPRACTICE: Which of the equations below define y as a function of x?a. b.
c. c.
FUNCTIONNOT A FUNCTION
NOT A FUNCTIONFUNCTION
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1.2 FUNCTIONS: VERTICAL LINE TESTPRACTICE: Identify which graphs are functions using the Vertical Line Test.
1. 2. 3.
4. 5. 6.
FUNCTION FUNCTION NOT A FUNCTION
NOT A FUNCTIONFUNCTION FUNCTION
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1.2 DOMAIN AND RANGE
Function Machine
input
output
𝒙
𝒚
DOMAIN
RANGE
Independent variable
Dependent variable
EXAMPLES:1. 2.
3.
DOMAIN: where the graph exists on the x-axis.RANGE: where the graph exists on the y-axis.
DOMAIN:RANGE:
DOMAIN:RANGE:
DOMAIN:RANGE:
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1.2 DOMAIN AND RANGEEXAMPLE 1: Find the domain and range, then sketch the graph of the function.1. 2.
3. 4.
DOMAIN:
RANGE:
DOMAIN:
RANGE:
DOMAIN:
RANGE:
DOMAIN:
RANGE:
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1.2 DOMAIN AND RANGEEXAMPLE 2: Use a graphing utility to graph the function. Then determine the domain and range of the function.1. 2.
3. 4.
DOMAIN:
RANGE:
DOMAIN:
RANGE:
DOMAIN:
RANGE:
DOMAIN:
RANGE:
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1.2 SYMMETRY-EVEN AND ODD FUNCTIONSA function is an…
EVEN FUNCTION if
ODD FUNCTION if
Symmetry: about the y-axis Symmetry: about the origin
(−𝑥 , 𝑦 ) (𝑥 , 𝑦 )
(−𝑥 ,− 𝑦 )(𝑥 , 𝑦 )
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1.2 SYMMETRY-EVEN AND ODD FUNCTIONSEXAMPLE: Determine whether the function is even, odd, or neither.1. 2.
3. 4.
EVEN ODD
NEITHER EVEN
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1.2 SYMMETRY-EVEN AND ODD FUNCTIONSEXAMPLE 2: Determine whether the function is even, odd, or neither without graphing.1. 2.
3. 4.
EVEN ODD
NEITHER
EVEN
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1.2 PIECEWISE FUNCTIONSDifferent functions defined in certain domains.
EXAMPLE:
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1.2 SYMMETRY-EVEN AND ODD FUNCTIONSEXAMPLE 2: Write a piecewise formula for the function.
(2 ,1)𝑓 (𝑥 )=¿ 0<𝑥≤2
2<𝑥≤5−𝑥+2 ,
¿−1
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HOMEWORK #2:
Pg.19: QR: 1-11odd E: 1-19odd, 21-30, 31-
35odd, 37-40, 44-45
If finished, work on other assignments:
HW #1: Pg.9: QR:1-9odd E:1-23odd, 27-33odd, 37, 41, 53