Identifying Functions by Analyzing Graphs

This lesson teaches how to identify functions by analyzing graphs. It covers the properties of functions, including whether a relation is a function, one-to-one, or has a constant rate of change. The lesson highlights common mistakes in plotting graphs, such as switching inputs and outputs. It explains how to determine if a graph represents a function, emphasizing that each input must have a unique output. The lesson also distinguishes between functions and one-to-one functions, noting that while a function can have shared outputs, a one-to-one function cannot. The session concludes with a recap of these concepts.

What is a common mistake when plotting input and output on a coordinate grid?

• Forgetting to label the axes

• Plotting on the Y-axis first

• Using the wrong scale

• Switching the input and output

Which of the following indicates a function has a constant rate of change?

• The graph is a straight line

• The graph is a circle

• The graph is a curve

• The graph has multiple peaks

What does it mean if a graph shows stacked points for the same input value?

• The graph is not a function

• The graph has a constant rate of change

• The graph is one-to-one

• The graph is a function

How can you tell if a function is not one-to-one?

• The graph is a parabola

• Each input has a unique output

• Different inputs share the same output

• The graph is a straight line

What is a characteristic of a function that is not one-to-one?

• The graph is a zigzag

• The graph is a circle

• Different inputs have the same output

• Each input has multiple outputs