Inverse Functions and Graphing

The video tutorial explains how to graph the inverse of a function by identifying and interchanging the coordinates of points on the original function's graph. It emphasizes the importance of the function being 1-to-1, verified by the horizontal line test, to ensure the inverse is also a function. The tutorial demonstrates plotting the inverse function and highlights the reflection property across the line y=x.

What is the first step in graphing the inverse of a function?

• Determine the slope of the tangent line

• Calculate the area under the curve

• Interchange the x and y coordinates of points on the function

• Find the derivative of the function

What does the horizontal line test determine?

• If a function is differentiable

• If a function is one-to-one

• If a function is periodic

• If a function is continuous

If a function is not one-to-one, what can be said about its inverse?

• The inverse is not a function

• The inverse is undefined

• The inverse is the same as the original function

• The inverse is a function

Which of the following is a property of one-to-one functions?

• They pass the horizontal line test

• They pass the vertical line test

• They are always linear

• They have multiple y-values for each x-value

Which of the following points is on the graph of f(x) if its inverse has the point (1, 2)?

• (2, 1)

• (1, 2)

• (2, 0)

• (0, 1)

What is the inverse point of (3, 4) on the graph of f(x)?

• (4, 3)

• (3, 4)

• (5, 3)

• (4, 5)

What is the y-intercept of the function f(x) if its inverse has the point (-5, 0)?

• (0, 5)

• (-5, 0)

• (5, 0)

• (0, -5)

How many points were used to graph the inverse function in the tutorial?

• Six

• Five

• Seven

• Four

What is the graphical relationship between a function and its inverse?

• They are reflections across the line y = x

• They are perpendicular lines

• They are identical

• They are parallel lines

Which line is used as the axis of reflection for a function and its inverse?

• x = y

• y = x

• x = 0

• y = 0