Understanding Inverse Functions

The video tutorial explains how to graph the inverse of a function, f inverse of x, by interchanging the x and y coordinates of points on the graph of f(x). It emphasizes the importance of the function being one-to-one, which can be verified using the horizontal line test. The tutorial demonstrates identifying points on f(x), interchanging their coordinates, and plotting them to graph f inverse of x. It also highlights the reflection property of f(x) and f inverse of x across the line y=x.

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

• Add a constant to all values

• Interchange the x and y values

• Divide all values by 2

• Multiply all values by -1

Why is it important for a function to be one-to-one to have an inverse?

• Because it allows for multiple outputs for a single input

• Because it makes the function easier to graph

• Because it ensures each output is unique to a single input

• Because it ensures the function is continuous

What test is used to determine if a function is one-to-one?

• Derivative test

• Horizontal line test

• Vertical line test

• Slope test

Which of the following points is on the graph of f inverse(x) if (3, 9) is on f(x)?

• (9, 3)

• (3, 9)

• (9, -3)

• (-3, 9)

What is the result of interchanging the x and y values of the point (-2, 0)?

• (0, -2)

• (-2, 0)

• (2, 0)

• (0, 2)

What property do the graphs of f(x) and f inverse(x) share when plotted on the same coordinate plane?

• They are parallel to each other

• They are reflections across the line y = x

• They intersect at the origin

• They are identical

Which line do the graphs of f(x) and f inverse(x) reflect across?

• y = x

• x = 0

• x = y

• y = 0

If a point on f(x) is (0, 2), what is the corresponding point on f inverse(x)?

• (-2, 0)

• (0, -2)

• (0, 2)

• (2, 0)

What should you do if you need more points to graph f inverse(x)?

• Find additional points on f(x) and interchange x and y

• Use only the intercepts

• Use the same points as f(x)

• Guess the points

What is a key characteristic of a cubic function in terms of its graph?

• It is always increasing

• It is always decreasing

• It has a constant slope

• It can pass the horizontal line test