Determining Functions - Pre Algebra

1. Why is $\{(1, 2), (2, 3), (1, 4)\}$ not a function?

   The input 1 is paired with two outputs, 2 and 4.

2. Why is the graph of $x = 3$ not a function?

   The input 3 is paired with every $y$-value, so a vertical line meets it at infinitely many points.

3. What value of $k$ makes $\{(3, 7), (4, 1), (3, k)\}$ a function?

   $k = 7$. The input 3 already has output 7, so it cannot have a different one.

4. What is the domain of a function?

   The set of all possible inputs.

5. Why is $\{(1, 5), (2, 5), (3, 5)\}$ a function even though every output is 5?

   Each input has only one output. Different inputs are allowed to share an output.

6. A table pairs inputs 1, 2, 2, 3 with outputs 4, 5, 6, 7. Which input keeps it from being a function?

   The input 2, which is paired with both 5 and 6.

7. What does the vertical line test say about a graph?

   If any vertical line crosses the graph more than once, the graph is not a function.

8. What makes a relation a function?

   Each input is paired with exactly one output.

9. Why is $y^2 = x$ not a function of $x$?

   The input $x = 4$ gives two outputs, $y = 2$ and $y = -2$.

10. When is a mapping diagram not a function?

    When any input has arrows to two or more different outputs.

11. Why is $y = x^2$ a function?

    Each $x$ gives exactly one $y$. Two inputs, like 2 and $-2$, may share an output.

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