Domain and Range

What do you remember ?

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Multiple Choice

Given g(x) = 4x - 7, find g(-9).

• g(-9) = 29

• g(-9) = -43

• g(-9) = 43

• g(-9) = -29

Multiple Choice

if k(x)= x+3 and k(x)=5

What is the value of x

• 2

• 8

• i don't know

Multiple Choice

All of the x values or inputs are called what?

• Domain
• Range

Multiple Choice

All of the y values or outputs are called what?

• Domain

• Range

A LOT of the time you can input any real number for x . This makes the domain= all real numbers or -∞ < x < ∞

BUT SOMETIMES certain numbers make no sense in the context of a situation

EXAMPLES :
*YOU CANNOT WORK A NEGATIVE NUMBER OF HOURS
* A CLASS CAN'T HAVE 25 AND A HALF STUDENTS

SO THE DOMAIN must be RESTRICTED.

Multiple Choice

Janice is working as a babysitter for the Harold Family. They plan to leave for their date at 7:00 pm and be back by 12:00 am. If the equation f(x) = 15x + 20 models the amount that Janice will earn, where x is the number of hours she works, and f(x) is the total money she earns, what is an appropriate domain for this situation?

• any value between 0 and 5

• any value between 15 and 20

• any value between -1 and 1

• any value greater than 0

Reminders

• WHOLE NUMBERS are the counting numbers including zero ( 0,1,2,3,4,5.....)

• INTEGERS:positive and negative whole numbers plus 0 ( ....-3,-2,-1,0,1,2,3...)

• RATIONAL NUMBER: any number that can be written as the ratio of two integers ( integers plus all terminating and repeating fractions/decimals

• IRRATIONAL NUMBERS: numbers that go on forever without repeating like π or √7

• REAL NUMBERS: all the numbers you've ever learned so far. ( rationals + irrationals

Multiple Choice

I throw a ball 10 feet in the air.  If the domain is the number of seconds, what is a possible range for the function?

• All real numbers between 0 and 10
• Integers between 0 and 10
• Whole Numbers between 0 and 10

Multiple Choice

The school is selling raffle tickets as a fundraiser. The profit from the tickets can be modeled by the equation P(x) = 3x - 35, where x is the number of tickets sold. Which best describes the possible domain?

• all real numbers greater than 0

• all whole numbers

• any rational number greater than 0

• all integers

When given an EQUATION... a LOT of time the domain is all real numbers but there are some restrictions

•You can NOT take the square root of a negative number

•You can NOT divide by zero

Multiple Choice

Which number would be excluded from the domain of

$$\frac{1}{x}+5$$  

•  all real numbers except x= 1

•  all real numbers except x= -1

•  all real numbers except x=5

•  all real numbers except x=0

Multiple Select

^{√(X-5). Which number(s) are NOT in the domain ( check all that apply)}

• 3

• 5

• 11

• -2

When you are given a graph and asked to describe the domain..... it's the amount of the x- axis needed to show entire graph.

think of it like cropping a picture. Where would the left and right boudaries be.

Multiple Choice

What is the domain of the graph?

Remember: Domain is the "x" values from left to right

• -7 ≤ x < 5

• -3 ≤ x < 1

• -3 ≤ y < 1

• -7 ≤ y < 5

Multiple Choice

What is the domain?

Remember domain is the "x" values.

And an open circle means it DOES NOT equal that number - use < and >

Only use ≤ and ≥ with a closed circle.

• -4 < x ≤ 5

• -4 ≤ x < 5

• -3 < y < 3

• -3 ≤ y ≤ 3

Multiple Choice

What is the domain?

• x = 2
• −∞ < x < ∞
• y = 2
• none of these

Multiple Choice

What is the domain of the graph?

• y≥1
• x ≥ 1
• All real numbers
• none of these

Multiple Choice

What is the domain of the graph?

• 
  

  $$\left\{x:-\infty<x<+\infty\right\}$$

• $$$$

• $$\left\{x:-3\le x\le3\right\}$$

Multiple Choice

What is the DOMAIN of this graph?

• x < -3

• x ≤ -3

• x > -3

• x ≥ -3

Multiple Choice

What is the DOMAIN of this graph? 
Remember:  DOMAIN is the x from left to right. 

• x < -3
• x ≤ -3
• x > -3
• x ≥ -3

Multiple Choice

What is the domain of this function?

• 1 ≤ f(x) ≤ 7
• 1 ≤ x ≤ 7
• -3 ≤ f(x) ≤ 3
• -3 ≤ x ≤ 3

Range describes all possible OUTPUTS

• graphically it is like cropping the image and giving the boundaries for y axis needed to see the entire graph.

• it describes the answers you will be getting out

Multiple Choice

What is the range of the graph?

Remember: Range is y!

• 1 ≤ x ≤ 5

• 1 < x < 5

• 1 ≤ y ≤ 5

• 1 < y < 5

Multiple Choice

What is the range? 

• [-∞, +∞]
• [-2, 2]
• (-∞, ∞)
• [0, 2]

Multiple Choice

What is the range?
Remember range is the "y" values (up and down) 
And an open circle means it DOES NOT equal that number - use < and >
Only use ≤ and ≥ with a closed circle. 

• -4 < x ≤ 5
• -4 ≤ x < 5
• -3 < y < 3
• -3 ≤ y ≤ 3

Multiple Choice

What is the range of this function?

• f(x) ≥ 0
• f(x) < 0
• x ≥ 0
• x < 0

Multiple Choice

What is the Range of this linear function?

• -6 ≤ y ≤ 6, integers

• 0 ≤ y ≤ 6, real numbers

• 0 ≤ y ≤ 6, integers

• 4 ≤ y ≤ 3, real numbers

Multiple Choice

What is the range of the graph?

• -2 < y < 10
• -3 < x < 3
• -2 ≤ y ≤ 10
• -3≤ x ≤ 3

Homework tonight is

1.1.3 # 34 and 35