When you're telling a story that involves two sets of numbers that are linked together—for example, about how an amount of money changes as time passes—it's handy to know about the different tools you can use to represent the situation so it's easier to understand.
You can use a table, an equation, and/or a graph to summarize the numbers and figure out the rate of change and initial value of the function. This knowledge is super helpful at school—and in many jobs that you could grow up to have!
Let's find out what you already know about functions. It's okay if you aren't sure of the answers to these questions because soon you'll watch a video about a teen who uses functions to keep track of his money. Then after you do some practice problems, you'll take another short quiz so you can compare how you did against where you started.
Kat and Xander estimate that they need $2,000 for their DJ equipment. Right now, they only have a total of $100 in savings. They decide to open a bank account to keep all the earnings from their birthday party business (so they're not tempted to spend it on something else). They estimate they'll earn an average of $50 per party. Which equation models the future growth of their account, where x = the number of parties worked and y = the bank account total?
Kat and Xander discussed how to charge families for their parties. They settled on a flat fee of $25 to plan the party plus $5 for each child at the party. Which graph accurately models their charging structure, where x = the number of children and y = the number of dollars charged?
Kat and Xander's business got off to a great start. The only difficulty they had was in bringing the right number of balloons. They often seemed to either have too many or not enough. Xander believed that there should be a set number of balloons per child at the party, plus some extras, just in case. Kat thought about it and developed an equation they could use. Here is the equation modeled as a graph:
Which equation correctly models this function?
The more Kat and Xander performed, the more word got around about their wonderful birthday parties as parents talked to each other. The duo began getting more and more calls each week requesting information about their parties. Kat made a graph to track their popularity.
What is the slope of this line?
To make their parties even more irresistible to little kids, Kat and Xander decided to add tethered balloon rides as an option for parents. The balloon holds 10 people, rises quickly to the maximum tether height of 50 meters, then slowly and steadily descends to the ground. As they tested their balloon, the pair took measurements to ensure a safe, smooth, and fun ride.
Two of the measurement points in (x, y) format, where x represents minutes in descent and y equals elevation (in meters) are (1, 45) and (4, 30). What is the y-intercept of this line?
Kat and Xander produced a techno version of Ring Around the Rosie. The bass line was fantastic, and it drove the little kids wild with excitement! Here is a table showing the number of beats heard in the music per minutes played. What is the slope of this line?
How confident are you about solving problems involving functions, slope (rate of change), and y-intercept (initial value)?
