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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

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

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Page 1: 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

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

Page 2: 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

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)

Page 3: 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

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.

Page 4: 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

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

Page 5: 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

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

Page 6: 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

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

Page 7: 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

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:

Page 8: 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

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:

Page 9: 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

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:

Page 10: 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

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 )

Page 11: 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

1.2 SYMMETRY-EVEN AND ODD FUNCTIONSEXAMPLE: Determine whether the function is even, odd, or neither.1. 2.

3. 4.

EVEN ODD

NEITHER EVEN

Page 12: 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

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

Page 13: 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

1.2 PIECEWISE FUNCTIONSDifferent functions defined in certain domains.

EXAMPLE:

Page 14: 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

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

Page 15: 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

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