Inverse Functions and Their Graphs

The video tutorial explains how to graph the inverse of a function, emphasizing the symmetry with the line y=2x. It provides techniques for sketching inverses of various functions, including parabolas and curves, by reflecting them across the y=2x line. The tutorial also offers practice questions to help learners visualize and understand the process of graphing inverse functions.

What is the line of symmetry for the graph of an inverse function?

• x = 2y

• y = 2x

• y = x

• y = -x

When graphing the inverse of a function, what is the first step?

• Calculate the slope

• Find the x-intercepts

• Draw a dotted line for y = 2x

• Draw the original function

How do the x-intercepts and y-intercepts change when finding the inverse of a function?

• They are halved

• They are swapped

• They are doubled

• They remain the same

In the example of sketching the inverse of a parabola, what is the key visual strategy?

• Focus on the vertex

• Ignore the x-intercepts

• Consider the axis of symmetry

• Flip parts of the graph across y = 2x

What should you check to ensure the inverse graph is correct?

• The graph is symmetrical about the y-axis

• The graph intersects y = 2x at the same points as the original

• The graph is below the x-axis

• The graph is above the x-axis

What is a useful technique when struggling to visualize the inverse graph?

• Consider only a portion of the graph

• Draw the graph in a different color

• Use a ruler to measure distances

• Ignore the y-intercepts

In the final exercise, what is emphasized about the relationship between the original and inverse graphs?

• They are unrelated

• They are identical

• They are always parallel

• They correspond to each other in specific parts