TODAY IN CALCULUS… WARM UP: Linear Equations multiple choice Learning Targets : You will be...

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

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)

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.

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

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

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

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:

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:

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:

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 )

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

3. 4.

EVEN ODD

NEITHER EVEN

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

1.2 PIECEWISE FUNCTIONSDifferent functions defined in certain domains.

EXAMPLE:

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

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