Understanding Inverse Functions and Their Graphs

The video tutorial explains how to graph the inverse of a one-to-one function. It begins by defining inverse functions and the concept of one-to-one functions. The tutorial then demonstrates how to graph the inverse by identifying points on the original function's graph and interchanging their x and y values. It highlights the importance of recognizing horizontal and vertical asymptotes and reflects the graph across the line y=x to verify accuracy.

What is the primary method to find the inverse of a function?

• Add a constant to all x-values

• Reflect the graph over the x-axis

• Interchange the x and y values in ordered pairs

• Multiply all y-values by -1

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

• It has a unique x-value for each y-value

• It passes the vertical line test

• It is symmetric about the y-axis

• It has a unique y-value for each x-value

Which test can be used to determine if a function is one-to-one?

• Derivative test

• Horizontal line test

• Slope test

• Vertical line test

What does the graph of f(x) do as it approaches the x-axis?

• It approaches but never touches the x-axis

• It touches the x-axis

• It moves away from the x-axis

• It becomes completely horizontal

What is the y-intercept of the function f(x) as mentioned in the video?

• 1

• 0

• 2

• 1/2

Which of the following is a point on the graph of f inverse(x) derived from f(x)?

• (1, 0)

• (0, 1)

• (3, 4)

• (2, 3)

What is the relationship between the graphs of f(x) and f inverse(x)?

• They are reflections across the x-axis

• They are reflections across the y-axis

• They are reflections across the line y = x

• They are identical

What type of asymptote does the graph of f inverse(x) have?

• Vertical asymptote at x = 1

• Horizontal asymptote at y = 1

• Vertical asymptote at x = 0

• Horizontal asymptote at y = 0

As the graph of f inverse(x) approaches the y-axis, what does it do?

• It approaches but never touches the y-axis

• It crosses the y-axis

• It moves away from the y-axis

• It touches the y-axis

What is the significance of the line y = x in relation to f(x) and f inverse(x)?

• It is the axis of symmetry for both graphs

• It is the line where both graphs are parallel

• It is the line where both graphs intersect

• It is the line of reflection for both graphs