Is the Relation a Function? (Graphical Analysis)

Q1. Determine whether the relation shown in the graph is a function.

Background

Topic: Functions and Relations (Graphical Representation)

This question tests your understanding of what makes a relation a function, specifically using the graph to decide if each input (x-value) corresponds to exactly one output (y-value).

Key Terms:

• Function: A relation in which each input (x-value) has exactly one output (y-value).

• Vertical Line Test: A graphical method to determine if a relation is a function. If any vertical line crosses the graph more than once, the relation is not a function.

Step-by-Step Guidance

1. Examine the graph and identify the shape or curve represented. Notice how the curve resembles an 'S' shape.

2. Recall the vertical line test: Imagine drawing vertical lines at various x-values across the graph.

3. Observe whether any vertical line would intersect the graph at more than one point. If so, the relation fails the test.

4. Think about what this means: If a vertical line hits the graph more than once, it means a single x-value is paired with multiple y-values, which is not allowed for functions.

Try solving on your own before revealing the answer!

Final Answer: The relation is NOT a function.

Using the vertical line test, you can see that some vertical lines intersect the graph at more than one point. This means the relation does not assign exactly one y-value to each x-value.