One-to-One Functions and Tests

The video tutorial introduces the concept of one-to-one functions, explaining that a function is one-to-one if each element in the range corresponds to exactly one element in the domain. The horizontal line test is used to determine if a function is one-to-one. Examples of functions that pass and fail this test are provided, including exponential functions and absolute value functions. The tutorial also introduces the vertical line test, emphasizing that a function must first be a valid function before it can be considered one-to-one.

What is the purpose of the horizontal line test?

• To determine if a function is continuous

• To identify the domain of a function

• To find the range of a function

• To check if a function is one-to-one

What does the horizontal line test help to identify?

• The symmetry of a function

• The one-to-one nature of a function

• The continuity of a function

• The periodicity of a function

Which of the following best describes a one-to-one function?

• The function is periodic

• The function is symmetric

• Each output corresponds to exactly one input

• Each input has multiple outputs

Which of the following is NOT a characteristic of a one-to-one function?

• The function is always increasing

• A horizontal line intersects the graph at most once

• Each output corresponds to exactly one input

• Each input has a unique output

What does it mean if a horizontal line intersects a graph at more than one point?

• The function is quadratic

• The function is linear

• The function is one-to-one

• The function is not one-to-one

What is the result of a horizontal line intersecting a graph at exactly one point?

• The function is not one-to-one

• The function is one-to-one

• The function is quadratic

• The function is periodic

Which type of function is guaranteed to pass the horizontal line test?

• Exponential functions

• Quadratic functions

• Absolute value functions

• Linear functions

Which function is an example of one that passes the horizontal line test?

• Absolute value function

• Quadratic function

• Cubic function

• Exponential function

Why does the absolute value function fail the horizontal line test?

• It is not continuous

• It is not differentiable

• It is not defined for all real numbers

• A horizontal line can intersect it at more than one point

What is the significance of the vertical line test?

• To find the range of a function

• To identify the domain of a function

• To check if a function is one-to-one

• To determine if a graph is a function