Understanding Functions and Their Properties

This lesson teaches how to identify functions by analyzing graphs. It covers the properties of functions, including being one-to-one and having a constant rate of change. Common mistakes, such as switching input and output, are discussed. The lesson explains how to determine if a graph represents a function or not, emphasizing that each input must have exactly one output. It also distinguishes between functions and one-to-one functions, where each input has a unique output.

What are the three key properties to determine if a relation is a function?

• Being a function, having multiple outputs, and being linear

• Being one-to-one, having a constant rate of change, and being quadratic

• Being a function, being one-to-one, and having a constant rate of change

• Having a constant rate of change, being quadratic, and having multiple outputs

What is a common mistake when plotting graphs?

• Using incorrect labels for axes

• Using the wrong scale

• Switching the input and output

• Plotting points in the wrong quadrant

What is the correct order when plotting ordered pairs on a graph?

• Output first, then input

• Input first, then output

• Plot both simultaneously

• It doesn't matter

In a one-to-one function, what is true about the inputs and outputs?

• Outputs can be shared among inputs

• Each input can have multiple outputs

• Each input has a unique output

• Inputs are always greater than outputs

How can you identify a function with a constant rate of change?

• The graph is a curve

• The graph is a straight line

• The graph has multiple outputs for each input

• The graph is a circle

What happens to the output when the input changes by one in a function with a constant rate of change?

• The output remains the same

• The output changes by a constant amount

• The output decreases

• The output doubles

What indicates that a graph is not a function?

• The graph has a constant rate of change

• The graph is a parabola

• The graph is a straight line

• The graph has stacked points for the same input

What is a characteristic of a graph that is not a function?

• It has multiple outputs for a single input

• It is a straight line

• It is a parabola

• It has a constant rate of change

What does it mean if a function is not one-to-one?

• It is not a function

• Multiple inputs share the same output

• It has multiple outputs for a single input

• It has a constant rate of change

In a non-one-to-one function, what is true about the outputs?

• Outputs are always greater than inputs

• Outputs can be shared among different inputs

• Outputs are always less than inputs

• Each output is unique to an input