Unit 1 – Item 5
Arlington received a new cell phone for his birthday. The function 𝑓(𝑥) gives the number of texts he can receive per hour, 𝑥. What does the function 𝑓(3) = 200 represent?
Unit 1: Item 1
Use the following sequence below to answer the questions that follow.
-13, -9, -5 …
Part A:
If this pattern continues, what would be the 20th term in the sequence?
Part B:
A group of students studied the pattern. Each student has developed an equation that would be used to find the nth term in the sequence. Which student has an equation that works?
Unit 1 – Item 2
Jennifer has $1000 in her college savings account. She wants to add $500 to the account per year.
Model the Situation: Write a linear function 𝑓(𝑡) to represent the total amount of money in Jennifer's account after 𝑡 years.
Unit 1 – Item 3
Sarah bought a starter tomato plant and is now checking the growth of her tomato plant for several weeks. She measures the height of the plant at different times and records the data in the table below.
Which of the following equations best models the height of the plant over time based on the data provided?
Unit 1 – Item 4
A company is tracking the amount of revenue (in thousands of dollars) they generate each month.
The revenue can be modeled by the linear function 𝑓(𝑥) = 2𝑥 + 3, where 𝑥 is the number of months since the company started tracking.
If the company plans to track the revenue for the first 12 months, what is the domain of the function? Write your answer using interval notation.
Considering that the company projects a maximum revenue of $27,000 within this period, what is the range of the function? Write your answer using interval notation.
Unit 1 – Item 6
Danielle is analyzing the cost of internet service providers in New York. She is using a mathematical model where CCC represents the monthly cost and GGG is the number of gigabytes used. She has determined that the monthly cost for one provider is best modeled by a linear function.
Select the linear function that represents the monthly cost of the provider when the cost per gigabyte is $2.50 and there is a monthly fee of $20.
Unit 1 – Item 7
The school is organizing a charity fundraiser to support a local community project. Students are responsible for tracking the donations received each day and representing the data as an
arithmetic sequence.
On the first day of the fundraiser, the school received $500 in donations. Each subsequent
day, the donations increased by $75. Construct an arithmetic sequence function to represent the daily donations.
Choose the arithmetic sequence below if the school received $1000 in donations and each subsequent day, the donations increased by $50.
Unit 1 – Item 8
A beautician borrowed some startup money to start her business. She charges each client a set amount for her services. The total profit 𝑃(𝑐) she makes after 𝑐 clients can be modeled by a linear function. The function is given by 𝑃(𝑐) = 50𝑐 − 200, where 𝑃(𝑐) represents the profit in dollars after 𝑐 clients.
Identify the following characteristics using interval and set notation where appropriate.
The slope:
The y-intercept:
The x-intercept:
The domain of the function:
The range of the function:
Intervals where the function is increasing or decreasing:
The positive and negative intervals of the function:
Interpret the key characteristics of the graph in the context of the beautician's profit. Explain
each characteristic from the previous question.
The slope:
The y-intercept:
The x-intercept:
The domain of the function:
The range of the function:
Intervals where the function is increasing or decreasing:
The positive and negative intervals of the function:
Graph of the function 𝑓(𝑡). Identify the key
characteristics of the graph, including the y-intercept, slope, and the domain and range based on the context.
Analyze and Compare: Compare the linear function you wrote to the function 𝑔(𝑡) = 1000(1 + 0.05)𝑡, which represents a different savings plan where Jennifer starts with the
same $1000 but adds 5% interest compounded annually instead of adding a fixed amount
each year.
Calculate and Conclude: Determine how many years it will take for Jennifer to save
$28,000 to attend her favorite school using her original plan.
Calculate and Conclude: Determine how much money Jennifer will have in 6 years
under both plans
Create a graph of the linear function 𝑃(𝑐) = 50𝑐 − 200.