Examples of relations that are *not* functions (Algebra 1 focus).

📚 Quick Study Guide

• 🔢 A function is a relation where each input (x-value) has exactly one output (y-value).
• 🗺️ To determine if a relation is a function, you can use the vertical line test on its graph. If any vertical line intersects the graph more than once, it's NOT a function.
• 📝 Relations can be represented as ordered pairs, tables, mappings, or graphs.
• 📉 A relation is *not* a function if any input (x-value) is associated with more than one output (y-value). For example, {(1,2), (1,3)} is not a function because the input 1 has two outputs, 2 and 3.
• 💡 In a table, check if any x-value repeats with different y-values. If it does, it's not a function.

🧪 Practice Quiz

1. Which of the following relations is NOT a function?
   1. {(0, 1), (1, 2), (2, 3), (3, 4)}
   2. {(0, 0), (1, 1), (2, 4), (3, 9)}
   3. {(0, 1), (1, 2), (0, 3), (2, 4)}
   4. {(0, -1), (1, 0), (2, 1), (3, 2)}
2. Which of the following graphs represents a relation that is NOT a function?
   1. A straight line with a positive slope.
   2. A parabola opening upwards.
   3. A vertical line.
   4. A horizontal line.
3. Consider the relation: x = $y^2$. Is this relation a function?
   1. Yes
   2. No
   3. It depends on the value of x
   4. Cannot be determined
4. Which of the following tables represents a relation that is NOT a function?

   1. x	y
      1	2
      2	4
      3	6

   2. x	y
      1	2
      2	2
      3	2

   3. x	y
      1	2
      1	3
      2	4

   4. x	y
      0	0
      1	1
      2	4

5. Which equation does *not* represent a function?
   1. $y = x + 5$
   2. $y = x^3$
   3. $x^2 + y^2 = 9$
   4. $y = |x|$
6. Which mapping diagram represents a relation that is NOT a function?
   1. One where each x-value points to a unique y-value.
   2. One where multiple x-values point to the same y-value.
   3. One where one x-value points to two different y-values.
   4. One where there are more y-values than x-values.
7. Given the set of ordered pairs {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)}, is this relation a function?
   1. Yes
   2. No
   3. Not enough information
   4. Only if x is positive