Questions: Is the following a one-to-one function?

Is the following a one-to-one function?
Transcript text: Is the following a one-to-one function?
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Solution

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Solution Steps

Step 1: Understand the Definition of a One-to-One Function

A function \( f \) is one-to-one if and only if \( f(a) = f(b) \) implies \( a = b \) for all \( a \) and \( b \) in the domain of \( f \). This means that no two different inputs can map to the same output.

Step 2: Analyze the Given Graph

Examine the graph of the function \( y = f(x) \). Check if there are any horizontal lines that intersect the graph at more than one point. If such a horizontal line exists, the function is not one-to-one.

Step 3: Apply the Horizontal Line Test

Draw horizontal lines across different values of \( y \) on the graph. Observe if any horizontal line intersects the graph at more than one point.

Final Answer

The given function is not one-to-one because there are horizontal lines (e.g., \( y = -2 \)) that intersect the graph at more than one point.

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