Relations and Functions: One Input, One Output

Work each one out before you check it. Every question has a scratch pad and a calculator.

1. Question 1

   The relation $R = \{(-2, 6),\ (0, 1),\ (3, 6),\ (0, -4),\ (7, 1)\}$ is given. Write down its domain and its range as sets. How many elements does each set have?

   elements in the domain:

   elements in the range:

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2. Question 2

   The relation $\{(1, 4),\ (5, 7),\ (2k - 1, 4)\}$ is not a function. Find $k$.

   $k =$

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3. Question 3

   The relation $\{(1, 7),\ (2, 9),\ (3, 7),\ (4, 5),\ (6, 9)\}$ is a function of its first component. Now take the second component of each pair as the input and the first as the output. How many of these new inputs are paired with more than one output?

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4. Question 4

   A quiz is scored in whole points from $0$ to $50$, and the score decides the letter grade: $0$–$24$ gives F, $25$–$34$ gives C, $35$–$42$ gives B, and $43$–$50$ gives A. Now take the letter grade as the input and the score as the output. How many outputs is the input B paired with?

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5. Question 5

   A relation pairs each integer $y$ with $-3 \le y \le 3$ with the input $x = y^2$, giving ordered pairs $(x, y)$. List the pairs. How many input values $x$ are paired with more than one output $y$?

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