Subjects algebra

Relation Representation E4E777

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1. **State the problem:** We have data from five teenagers about hours babysat (x) and amount earned (y). We need to represent this relation using ordered pairs, a table, a mapping, and find domain and range. 2. **Write the set of ordered pairs:** Each ordered pair is $(x,y)$ where $x$ is hours babysat and $y$ is amount earned. Given points: $(3,40)$ Lee, $(4,35)$ Chantel, $(3,30)$ Reynaldo, $(1,20)$ Eliza, $(1,10)$ Jordan. So the set is $$\{(3,40),(4,35),(3,30),(1,20),(1,10)\}$$ 3. **Complete the table and mapping:** Table: $$\begin{array}{c|c} x & y \\\hline 1 & 10 \\ 1 & 20 \\ 3 & 30 \\ 3 & 40 \\ 4 & 35 \end{array}$$ Mapping diagram pairs each domain element to its range values: - $1 \to 10, 20$ - $3 \to 30, 40$ - $4 \to 35$ 4. **Write domain and range:** Domain is the set of all $x$ values: $$\{1,3,4\}$$ Range is the set of all $y$ values: $$\{10,20,30,35,40\}$$ 5. **Interpret from graph who babysat same hours:** Points with same $x$ coordinate mean same hours babysat. Here, Lee and Reynaldo both have $x=3$ hours. Eliza and Jordan both have $x=1$ hour. Chantel has $x=4$ hours alone. This shows which teenagers babysat the same number of hours. Final answer: - Ordered pairs: $\{(3,40),(4,35),(3,30),(1,20),(1,10)\}$ - Domain: $\{1,3,4\}$ - Range: $\{10,20,30,35,40\}$ - Same hours babysat: Lee & Reynaldo (3 hours), Eliza & Jordan (1 hour)