Question

ticket sales the set of ordered pairs below represents the number of tickets sold for a fundraiser. the x-coordinates represent the day and the y-coordinates represent the number of tickets sold on that day. draw a mapping diagram of the relation. is the relation a function? {(1,17), (2,19), (3,19), (4,23), (5,29)} which mapping diagram represents the relation? a. image of mapping diagram a b. image of mapping diagram b c. image of mapping diagram c d. image of mapping diagram d

Explanation:

Step1: Recall Function Mapping Rules

A function mapping requires each input (x - value, day) to map to exactly one output (y - value, tickets sold). So we check each mapping diagram to see if each x (1,2,3,4,5) maps to its corresponding y (17,19,19,23,29) without any input having multiple outputs or incorrect mappings.

Step2: Analyze Option A

• Inputs (x): 1,2,3,4,5 (assuming the top oval has these, though some labels are unclear, but let's check mappings). Wait, no, looking at the ordered pairs: (1,17), (2,19), (3,19), (4,23), (5,29). So x = 1 → 17, x = 2 → 19, x = 3 → 19, x = 4 → 23, x = 5 → 29. Now check the mapping diagrams:
• Option A: Top oval (x) should have 1,2,3,4,5? Wait, maybe the top is x (days 1 - 5) and bottom is y (tickets 17,19,23,29). Wait, the ordered pairs are (1,17), (2,19), (3,19), (4,23), (5,29). So for x = 1, map to 17; x = 2 to 19; x = 3 to 19; x = 4 to 23; x = 5 to 29. Now check the diagrams:
• Option A: Let's see the top oval (x) has 1,2,3,4,5? Wait, maybe the first diagram (A) has x - values 1,2,3,4,5 (or similar) and maps 1→17, 2→19, 3→19, 4→23, 5→29? Wait, no, maybe I misread. Wait the correct mapping should have each x (1,2,3,4,5) map to their y - values. Let's check each option:
• Option A: If the top is x (1,2,3,4,5) and bottom is y (17,19,23,29, etc.). Wait, the ordered pairs are (1,17), (2,19), (3,19), (4,23), (5,29). So x = 1 → 17, x = 2 → 19, x = 3 → 19, x = 4 → 23, x = 5 → 29. Now look at the mapping diagrams:
• Option A: The top oval (x) has some numbers, and the bottom (y) has 17,19,23,29 (and maybe 19 again? Wait, (2,19) and (3,19) are both 19, so x = 2 and x = 3 both map to 19, which is allowed in a function (multiple inputs can map to same output, but each input maps to one output). Now check the arrows:
• Wait, maybe the correct diagram is the one where x = 1 → 17, x = 2 → 19, x = 3 → 19, x = 4 → 23, x = 5 → 29. Looking at the options, Option A's mapping: Let's assume the top is x (1,2,3,4,5) and bottom is y (17,19,23,29,19? No, 19 is repeated for x = 2 and 3. Wait, the ordered pairs are (1,17), (2,19), (3,19), (4,23), (5,29). So the mapping should have:
• 1 → 17
• 2 → 19
• 3 → 19
• 4 → 23
• 5 → 29

Now check the diagrams:

• Option A: The top oval (x) has 1,2,3,4,5 (or similar) and the bottom (y) has 17,19,23,29 (and maybe 19? Wait, no, 19 is the y - value for x = 2 and 3. So in the mapping, x = 2 and x = 3 both point to 19, which is okay (function allows multiple inputs to same output, as long as each input has one output). Now check the other options:
• Option B: Top is y (17,19,23,29) and bottom is x (1,2,3,4,5)? No, because mapping should be x→y, not y→x. So B is reversed, so incorrect.
• Option C: Top is y? No, same as B, reversed? Wait, no, the top should be x (days) and bottom y (tickets). So C and D have top as y? No, maybe not. Wait, the ordered pairs are (x,y), so x is first, so mapping is x (top) → y (bottom). So Option A: top is x (1,2,3,4,5) and bottom is y (17,19,23,29, etc.), with arrows: 1→17, 2→19, 3→19, 4→23, 5→29. That matches the ordered pairs. Option B: top is y, bottom is x, so reversed, so incorrect. Option C: top is y? No, and mappings seem reversed. Option D: top is y, bottom is x, reversed. So the correct mapping diagram is Option A.

Answer:

A (the mapping diagram labeled A)