Question

make an arrow diagram to represent the relation shown in the table. is the relation a function? explain.| input | output || ---- | ---- || 1 | 2 || 11 | 32 || 15 | 2 || 16 | 32 |which figure is the arrow diagram of the relation shown?○ a.○ b.○ c.○ d.view an example video get more helpclear allcheck answer

Explanation:

Step1: Match inputs to outputs

From the table:

• Input $1$ → Output $2$
• Input $11$ → Output $32$
• Input $15$ → Output $2$
• Input $16$ → Output $32$

Step2: Compare to options

Check which diagram maps inputs (left oval) to outputs (right oval) correctly:

• Option A: $1→2$, $11→2$, $15→32$, $16→32$ (incorrect matches)
• Option B: Swaps input/output ovals (incorrect structure)
• Option C: $1→2$, $11→2$, $15→32$, $16→32$ (incorrect matches)
• Option D: $2→1$, $11→1$, $15→32$, $16→32$ (swapped, incorrect)

Correct mapping: Left oval (inputs: 1,11,15,16) → Right oval (outputs:2,32) with $1→2$, $15→2$, $11→32$, $16→32$, which matches Option A's structure with corrected arrows, but Option A has wrong arrow targets. Recheck: The correct diagram is the one where inputs 1,15 point to 2; 11,16 point to 32. This is Option A's layout but with arrows fixed, but among given options, Option A is the only one with inputs on left, outputs on right, and the correct pairings (the arrows in A are misdrawn in the image? No, re-read: The table input 1→2, 11→32,15→2,16→32. So Option A has 1→2, 11→2, 15→32,16→32 (wrong). Option C has 1→2,11→2,15→32,16→32 (wrong). Wait, no: Option A's arrows: 1→2, 11→2,15→32,16→32. Option C's arrows:1→2,11→2,15→32,16→32. Wait, no, the correct mapping is 1→2,15→2,11→32,16→32. So the correct diagram is the one where 1 and 15 point to 2; 11 and 16 point to 32. This is Option A** if the arrows for 11 and 15 are swapped. But among the options, the only one with inputs on left, outputs on right is A. Then, check if it's a function: A relation is a function if each input has exactly one output. Each input (1,11,15,16) has only one output, so it is a function.

Answer:

Correct arrow diagram: A. (with corrected arrow mappings: 1→2, 15→2, 11→32, 16→32; among given options, A is the only one with inputs on left, outputs on right)
The relation is a function. Each input has exactly one corresponding output, which satisfies the definition of a function.