How to determine if a function graph has an inverse and if the inverse is a function

The video tutorial explains the concept of functions, focusing on the vertical line test to determine if a graph represents a function. It introduces one-to-one functions, which require the horizontal line test to verify if a function has an inverse. The tutorial also covers graphing inverse functions by reflecting over the y=x line and discusses scenarios where inverses do not exist.

What is the purpose of the vertical line test in determining a function?

• To ensure each input has exactly one output

• To determine if a function is increasing

• To check if a graph is symmetric

• To find the slope of a line

What does it mean for a function to be one-to-one?

• The function is symmetric

• Each input has multiple outputs

• Each output has multiple inputs

• Each input has exactly one output and each output has exactly one input

Which test is used to determine if a function has an inverse?

• Vertical line test

• Symmetry test

• Slope test

• Horizontal line test

How can you graph the inverse of a function?

• By rotating the graph 90 degrees

• By reflecting the graph over the line y = x

• By stretching the graph horizontally

• By shifting the graph upwards

What happens when a graph is reflected over the line y = x?

• It becomes a vertical line

• It remains unchanged

• It produces the inverse graph

• It becomes a horizontal line

Why is the horizontal line test important in determining the existence of an inverse?

• It verifies the graph is continuous

• It ensures each output has exactly one input

• It checks if the graph is symmetric

• It determines the slope of the graph

What does it indicate if a graph fails the horizontal line test?

• The function is symmetric

• The function is not continuous

• The function does not have an inverse

• The function is not defined