WARM-UP — 5 MINUTES

Function or Not? You Decide!

Sort these into two piles at your desk!

Set A

{(1, 3), (2, 5), (3, 7)}

Function? ____

Set B

{(1, 4), (2, 7), (1, 9)}

Function? ____

Set C

{(5, 2), (6, 2), (7, 2)}

Function? ____

Set D

{(3, 1), (3, 2), (3, 3)}

Function? ____

Hint: Check if any x-value REPEATS with different y-values!

I DO — EXPLICIT INSTRUCTION

A Function is Like a Vending Machine 🏪

🏪 VENDING

Each BUTTON gives
EXACTLY ONE item!

A1

A2

A3

B1

B2

B3

Button A1 → always chips
Button B2 → always water

Each x (input) → only ONE y (output) = FUNCTION

Dallas Example

✅ Each student ID # → one student name = FUNCTION

❌ One phone number → multiple people = NOT a function

📏 Vertical Line Test (for graphs)

"If a vertical line touches the graph more than once at any spot → NOT a function!"

Same y is OK! → {(1,5), (2,5), (3,5)} IS a function (each x is different)

I DO / WE DO — SCATTERPLOTS IN DESMOS

Dallas Temperature vs Ice Cream Sales 🍦

Month	Temp (°F)	Ice Cream Sales
Jan	45	120
Mar	62	210
May	78	340
Jul	95	480
Sep	85	400
Nov	55	160

🖩 Desmos Steps

1. Press + → click "table"

2. Enter Temp as x, Sales as y

3. Click "Add regression"

4. Read: m = slope (how much sales change per degree)

As temp goes UP, sales go UP → POSITIVE association!

Types of Association

📈 Positive
Both go UP together

📉 Negative
One up, other DOWN

🤷 None
No pattern at all

Making Predictions

"If it's 95°F in July, trace UP to the trend line — how many ice cream sales?"

The regression equation lets you predict values you don't have!

WE DO — GUIDED PRACTICE: FUNCTIONS

Is It a Function? 🤔

Problem 1

{(2, 5), (3, 7),
(4, 9), (5, 11)}

x-values: 2, 3, 4, 5 ✅
Any repeat? NO ✅
→ YES, function! ✅

Problem 2

{(1, 4), (2, 7),
(1, 9), (3, 5)}

x-values: 1, 2, 1, 3 ✅
Any repeat? ____
→ Function? ____

Problem 3

{(4, 2), (5, 8),
(6, 2), (7, 10)}

x-values: ________
Repeat? ____
→ Function? ____

📋 Function Checklist:
☐ List ALL x-values
☐ Does any x REPEAT?
☐ If repeat → different y's? → NOT a function
☐ No repeats → IS a function!

⚠️ Tricky Part:
Same y is OK! → {(1,5), (2,5)} IS a function
Same x with different y's → NOT a function!

WE DO — SCATTERPLOT PREDICTION

Dallas Mavericks: Games vs Points 🏀

🏀 Use Desmos to find the trend and make a prediction!

Games (x)	Total Points (y)
2	220
5	540
8	870
10	1080
12	1300

Step 1: Press + → table → enter data ✅

Step 2: Click "Add regression" ✅

Step 3: Association type? (positive/negative/none): __________

Step 4: Desmos equation: y = ____x + ____

Step 5: Predict — after 20 games, total points ≈ ________

📌 Day 3 Reference — Identifying Functions

🎫 Exit Ticket — Day 3

1. Which set of ordered pairs represents a function?

A. {(1, 3), (2, 5), (1, 7), (4, 9)}

B. {(1, 3), (2, 5), (3, 7), (4, 9)}

C. {(5, 1), (5, 2), (5, 3), (5, 4)}

D. {(2, 4), (3, 6), (2, 8), (4, 10)}

2. A scatterplot shows that as the temperature in Dallas increases, water park attendance also increases. What type of association does this show?

A. Positive association

B. Negative association

C. No association

D. Non-linear association