Topic 2 Performance Task Reteach

Topic 2 Performance Task Reteach

You will need to take notes as you complete this. Without the notes, you will not be able to retest.

​Function Notation

​* Read as "f of x". This is a way to name a function.

​* You are replacing the y with f(x).

Multiple Choice

Joey has $50 in his lunch account. He spends $3 on lunch everyday. Pick the equation below that represents this in function notation.

• $$f(x)=3x+50$$  

• $$f\left(x\right)\ =\ 50x\ -3$$  

• $$f\left(x\right)=-3x+50$$  

• $$y\ =50-3x$$  

Open Ended

Eliza is making bracelets to sell. The cost of her supplies is $40.25. She plans to sell the bracelets for $5 each. Write an equation using function notation to represent Eliza's profit for selling any number of bracelets.

​Define your variables

​* When you are writing an equation, it is important that you define your variables. This helps others understand what you are trying to represent.

​* If we think back to our test, we had the problem: The Perry volleyball team is buying new uniforms. Each uniform is $12.50 and there is a shipping cost of $9. They can have at least 8 students on the team, but no more than 16. (This last sentence is only to help us with domain and range). Our function should have been f(x) = 12.50x + 9 . So we need to define the variables so we know what each represents.

​x : number of uniforms

​f(x) or y: Total cost

Multiple Choice

 You try:  If we look at the last problem I gave you. Joey has $50 in his lunch account. He spends $3 on lunch everyday. The correct function was f(x)= -3x+50

​ * What does the x represent in this problem? What does f(x) represent? (hint: when you read the equation, replace the variable with the meaning to see if it makes sense.)

• x: Cost of lunch

  f(x): How much money he starts with

• x: number of days

  f(x): Money in his lunch account

• x: Cost of lunch

  f(x): number of days

• x: money in his lunch account

  f(x): number of days

Open Ended

Eliza is making bracelets to sell. The cost of her supplies is $40.25. She plans to sell the bracelets for $5 each. You wrote the equation on slide 4. What would your variables represent in this problem?

​Solving Equations in function notation

• ​When given f(3) -> This means to substitute 3 every where for x. You can also go to your table and find the y-value when x = 3.

• ​When given f(x) = 5 -> This means you substitute 5 in for y. you can go to your table and find the x-value when y = 5.

Multiple Choice

Joey has $50 in his lunch account. He spends $3 on lunch everyday.  Find f(11). 

• $$f(11)=17$$  

• $$f\left(11\right)\ =\ 13$$  

• $$f\left(13\right)=11$$  

• $$f\left(17\right)\ =11$$  

​On the previous slide, you were finding f(11). What does that mean in the context of this problem?

Open Ended

Eliza is making bracelets to sell. The cost of her supplies is $40.25. She plans to sell the bracelets for $5 each.  Find  $$f\left(7\right)$$  .

Multiple Choice

Joey has $50 in his lunch account. He spends $3 on lunch everyday. Find x when f(x) = 32

• x = 15

• x = 4

• x = 8

• x = 6

​In the last problem you were trying to find x when f(x) = 32.

​* This tells you that you need to go to your table and look at the y values and find where y = 32. Whatever the x value (or input) gives you 32 is your answer.

​* This tells me that when x = 6, then y = 32. In the context of this problem this means that after 6 days, Joey will have $32 left in his account.

Open Ended

Eliza is making bracelets to sell. The cost of her supplies is $40.25. She plans to sell the bracelets for $5 each.   Find x when f(x) = 9.75, and then explain what this means in the context of this problem.

​Continuous or Discrete

​When we are trying to determine if something is

​continuous or discrete, we need to think about

​questions such as:

​1.) Does it make sense to have half of this? 1/8 of this? Or any portion?

​2.) Does it makes sense at any value?

​On our performance task, we spoke about whether the uniforms and cost was continuous or discrete. Since we can't buy half a uniform it is discrete.

Multiple Choice

Joey has $50 in his lunch account. He spends $3 on lunch everyday.  Is this data continuous or discrete?

• Continuous

• Discrete

Open Ended

Eliza is making bracelets to sell. The cost of her supplies is $40.25. She plans to sell the bracelets for $5 each.  Is this data continuous or discrete? Explain your reasoning.

​Domain and Range

​*If the data is continuous it is written as an inequality

​or compound inequality.

​* If the data is discrete, it is written as a list.

Multiple Choice

Joey has $50 in his lunch account. He spends $3 on lunch everyday.  If Joey wants to make a table that shows his lunch account for the first 5 days, which of the following shows this?  

Open Ended

Eliza is making bracelets to sell. The cost of her supplies is $40.25. She plans to sell the bracelets for $5 each.  State the domain and range for the first 4 days she makes a profit (She is making positive money).

Now you will try a few on your own.

​

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?

• any value between 0 and 5
• any value between 15 and 20
• any value between -1 and 1
• any value greater than 0

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 range?

• any value between 0 and 20
• any value between 0 and 125
• any value between 0 and 95
• any value greater than 0

Multiple Choice

The student council sent its members on four field trips during the school year. The number of buses needed to transport the members on each trip is a function of the number of members who went on each trip. This function consists only the ordered pairs (52, 3), (72, 4), (86, 5), and (105, 6). What is the domain for this situation?

• {52, 105}

• {3, 4, 5, 6}

• {52, 72, 86, 105}

• {3, 4, 5, 6, 52, 72, 86, 105}

Multiple Choice

A student rode a bike from school to a recreation center. The graph shows the student's distance in miles from the recreation center after riding the bike for x minutes. What is the range of the function for this situation? HINT: what are the smallest and biggest y values the line touches?

• All real numbers greater than or equal to 0 and less than or equal to 28.

• All real numbers greater than or equal to 0 and less than or equal to 9.

• All real numbers less than or equal to 28.

• All real numbers less than or equal to 9.

Multiple Choice

A student is taking a test that has 20 questions on it. The student's score is a function of how many questions he misses: f(x)=100-5x, where x is the number of questions incorrect. If the student misses between 7 to 11 questions, What is the domain and range?

• Domain: {7, 8, 9, 10 ,11}

  Range: {65, 60 55, 50, 45}

• Domain: {7, 8, 9, 10 ,11}

  Range: {45, 50, 55, 60, 65}

• Domain: 7< x<11
  Range: 45<y< 65

• Domain: $$7\le x\le11$$ Range: $$45\le y\le65$$