Determine whether each function graphed or defined is one-to-one.

Verified step by step guidance

1. Step 1: Understand the definition of a one-to-one function. A function is one-to-one if and only if every horizontal line intersects the graph of the function at most once.
2. Step 2: Observe the given graph carefully. Notice the shape and direction of the curve.
3. Step 3: Apply the Horizontal Line Test. Imagine drawing horizontal lines across different parts of the graph.
4. Step 4: Check if any horizontal line intersects the graph more than once. If no horizontal line intersects the graph more than once, the function is one-to-one.
5. Step 5: Conclude whether the function is one-to-one based on the results of the Horizontal Line Test.

Key Concepts

One-to-One Function

A one-to-one function is a type of function where each output value corresponds to exactly one input value. This means that no two different inputs produce the same output. To determine if a function is one-to-one, one can use the horizontal line test: if any horizontal line intersects the graph of the function more than once, the function is not one-to-one.

Horizontal Line Test

The horizontal line test is a visual method used to determine if a function is one-to-one. If a horizontal line drawn across the graph of the function intersects the graph at more than one point, the function fails the test and is not one-to-one. This test is particularly useful for analyzing the behavior of functions graphically.

Graph Interpretation

Graph interpretation involves analyzing the features of a graph to extract meaningful information about the function it represents. This includes identifying key characteristics such as intercepts, increasing or decreasing intervals, and symmetry. Understanding how to read and interpret graphs is essential for determining properties like whether a function is one-to-one.