Function Values in School Projects

Interpreting Real-World Functions Algebra 1 Basketball Courts vs. Picnic Areas

What Are Function Values?

Functions describe relationships between variables Input values (x) produce output values f(x) Real-world functions help us make decisions Today: School project planning with math!

Basketball Court Function: B(x) = 18,000x + 12,000

B(x) = total cost to build x basketball courts Fixed cost: $12,000 (planning and permits) Variable cost: $18,000 per court Let's interpret B(1) and B(2)!

Calculate: What Does B(1) and B(2) Mean?

B(1) = 18,000(1) + 12,000 = $30,000 This means: 1 basketball court costs $30,000 B(2) = 18,000(2) + 12,000 = $48,000 This means: 2 basketball courts cost $48,000

Upgrade Comparison: Basketball vs. Picnic Areas

{"left":"Basketball Courts: B(2) = $48,000, B(3) = $66,000\nPicnic Areas: P(2) = $35,000, P(3) = $50,000","right":"Cost difference B(3) - P(3) = $16,000\nBasketball courts cost more but serve different needs"}

Student Usage Over Time

Budget Function: f(x) = x ÷ 2,000

f(x) = number of features we can build with budget x Each feature costs $2,000 to add f(10,000) = 10,000 ÷ 2,000 = 5 features How many features can we build with $20,000?

Student Challenge: Solve f(20,000)

Given: f(x) = x ÷ 2,000 Calculate: f(20,000) = ? f(20,000) = 20,000 ÷ 2,000 = 10 features With $20,000, we can build 10 additional features!

Critical Thinking: Which Project is Better?

Consider all the data we've analyzed Think about: Cost, student usage, and school needs Basketball courts: Higher cost, active recreation Picnic areas: Lower cost, social gathering space

Summary: Functions Help Us Make Smart Decisions

Function values give us specific information Real-world contexts make math meaningful We can compare costs and benefits using math Great job interpreting functions today!