Analyzing One-to-One Functions Using Graphs

Q1. Determine whether the function graphed is one-to-one.

Background

Topic: One-to-One Functions (Injective Functions)

This question tests your understanding of what it means for a function to be one-to-one, and how to use the graph to determine this property.

Key Terms and Formulas:

• One-to-One Function: A function is one-to-one if each y-value is paired with exactly one x-value. In other words, no two different x-values produce the same y-value.

• Horizontal Line Test: A function is one-to-one if and only if every horizontal line intersects the graph at most once.

Step-by-Step Guidance

1. Examine the graph and identify the general shape of the function. Is it linear, quadratic, or another type?

2. Recall the horizontal line test: Draw or imagine horizontal lines (lines parallel to the x-axis) across the graph.

3. Observe whether any horizontal line crosses the graph at more than one point. If so, the function is not one-to-one.

4. Think about what this means: If a horizontal line intersects the graph more than once, it means there are multiple x-values that produce the same y-value.

Try solving on your own before revealing the answer!

Final Answer: No, the function is not one-to-one.

There are horizontal lines (for example, $y = 4$) that intersect the graph at more than one point. This means the function fails the horizontal line test and is not one-to-one.