Is It a Function? Algebra 1 Challenge Using the Vertical Line Test

📚 Quick Study Guide

• 🔢 A function is a relation where each input (x-value) has only one output (y-value).
• 📈 The Vertical Line Test is a visual method to determine if a graph represents a function.
• 🧪 If any vertical line intersects the graph more than once, the graph is not a function.
• 📝 Algebraically, ensure that for every $x$ value, there is only one corresponding $y$ value.
• 💡 If an equation can be manipulated to produce two or more $y$ values for a single $x$ value, it's not a function.

🤔 Practice Quiz

1. Which of the following graphs represents a function?
   1. A graph with a vertical line intersecting it at two points.
   2. A graph with a horizontal line intersecting it at one point.
   3. A graph that is a perfect circle.
   4. A graph where every vertical line intersects it at only one point.


2. Which equation represents a function?
   1. $x = y^2$
   2. $y = x^2$
   3. $x^2 + y^2 = 4$
   4. $x = |y|$


3. Does the set of ordered pairs {(1, 2), (2, 3), (3, 4), (1, 5)} represent a function?
   1. Yes, because all y-values are different.
   2. No, because the x-value 1 is associated with two different y-values.
   3. Yes, because all x-values are positive.
   4. No, because the y-values are consecutive.


4. Which of the following is NOT a function?
   1. $y = 3x + 2$
   2. $y = \frac{1}{x}$
   3. $x^2 + y^2 = 9$
   4. $y = |x|$


5. Which of the following mappings is a function?
   1. A student to their favorite color.
   2. A student to their test scores.
   3. A test score to the students who achieved it.
   4. A person to their siblings.


6. Which graph passes the vertical line test?
   1. A parabola opening to the side.
   2. A vertical line.
   3. A hyperbola $xy=1$.
   4. A circle.


7. Given the relation {(4, 2), (9, 3), (4, -2), (9, -3)}, is this a function?
   1. Yes, because each x-value has a corresponding y-value.
   2. No, because some x-values have more than one y-value.
   3. Yes, because the y-values include both positive and negative numbers.
   4. No, because the numbers are not consecutive.