vertical line test
definition →
yes or no are the graphed relations functions?
four graphs with yes or no and explain sections
exit ticket
quick write: which strategy do you prefer to determine if a relation is a function, a mapping diagram or the vertical line test? why?

Question

vertical line test
definition →
yes or no  are the graphed relations functions?
four graphs with yes or no and explain sections
exit ticket
quick write: which strategy do you prefer to determine if a relation is a function, a mapping diagram or the vertical line test? why?

Accepted Answer

### First Graph (Oval)
# Explanation:
## Step1: Recall Vertical Line Test
A relation is a function if no vertical line intersects its graph more than once.
## Step2: Apply to Oval Graph
For the oval graph, a vertical line (e.g., the y - axis) will intersect the oval at two points. So, it fails the vertical line test.
# Answer: NO. Explanation: A vertical line intersects the oval graph at more than one point, so it is not a function.

### Second Graph (V - shaped)
# Explanation:
## Step1: Recall Vertical Line Test
A relation is a function if no vertical line intersects its graph more than once.
## Step2: Apply to V - shaped Graph
For the V - shaped graph, any vertical line will intersect the graph at most once. So, it passes the vertical line test.
# Answer: YES. Explanation: No vertical line intersects the V - shaped graph more than once, so it is a function.

### Third Graph (Scattered Points)
# Explanation:
## Step1: Recall Function Definition for Discrete Points
A relation (set of ordered pairs) is a function if each input (x - value) has exactly one output (y - value).
## Step2: Analyze x - values
Looking at the x - values of the points, we can see that there are no repeated x - values with different y - values. Each x is paired with only one y.
# Answer: YES. Explanation: Each x - value is paired with exactly one y - value, so it is a function.

### Fourth Graph (Scattered Points)
# Explanation:
## Step1: Recall Function Definition for Discrete Points
A relation (set of ordered pairs) is a function if each input (x - value) has exactly one output (y - value).
## Step2: Analyze x - values
Looking at the x - values of the points, we can see that there are repeated x - values with different y - values (e.g., the x - value corresponding to the middle - top and middle - bottom points). So, it is not a function.
# Answer: NO. Explanation: There are x - values that are paired with more than one y - value, so it is not a function.

### Exit Ticket (Preference between Mapping Diagram and Vertical Line Test)
# Brief Explanations:
If we prefer the vertical line test: The vertical line test is straightforward for graph - based relations. It provides a visual and quick way to check if a graph represents a function by seeing if any vertical line intersects the graph more than once. For graphs (both continuous and discrete, when we can imagine the graph), it is very intuitive.

If we prefer mapping diagrams: Mapping diagrams show the relationship between the domain (input) and range (output) sets clearly. For discrete relations (sets of ordered pairs), we can easily see if each element in the domain is mapped to exactly one element in the range, without having to visualize a graph.

(Example of choosing vertical line test)
# Answer: I prefer the vertical line test. Because for a graphed relation, it is a very visual and quick method. By simply imagining or drawing vertical lines on the graph, we can immediately tell if any x - value has more than one y - value associated with it, which determines if the relation is a function.

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QUESTION IMAGE

Question

Explanation:

First Graph (Oval)

Step1: Recall Vertical Line Test

Step2: Apply to Oval Graph

Step1: Recall Vertical Line Test

Step2: Apply to V - shaped Graph

Step1: Recall Function Definition for Discrete Points

Step2: Analyze x - values

Answer:

Second Graph (V - shaped)