Reflections and Inverses in Functions

The video tutorial explores the concepts of domain and range, focusing on their properties and restrictions. It discusses how domain and range swap in inverse functions and highlights the geometric properties involved. The tutorial also covers visualizing reflections of functions across the line y = x, providing practical techniques for reflecting shapes using a ruler and understanding symmetry.

What are the domain and range of the original function discussed in the video?

• Domain: all real values, Range: all real values

• Domain: x > 0, Range: y > 0

• Domain: x < 0, Range: y < 0

• Domain: x = 0, Range: y = 0

How does a domain restriction in the original function affect its inverse?

• It becomes a new function altogether.

• It has no effect on the inverse.

• It remains a domain restriction in the inverse.

• It becomes a range restriction in the inverse.

What is the geometric property discussed that involves domain and range?

• They remain the same for both function and inverse.

• They are halved in the inverse.

• They are doubled in the inverse.

• They are swapped between the function and its inverse.

What line is used for reflecting functions and their inverses?

• x = 0

• y = 0

• x = y

• y = x

What is the angle formed by the line y = x?

• 60 degrees

• 45 degrees

• 90 degrees

• 30 degrees

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

• They are parallel.

• They are reflections across the line y = x.

• They are identical.

• They are perpendicular.

What happens to the intercepts when reflecting across y = x?

• The intercepts double.

• There are two intercepts.

• There is only one intercept.

• There are no intercepts.

What tool is suggested to help visualize reflections?

• A compass

• A calculator

• A protractor

• A ruler

What is the first step in creating a reflection of a point across a line?

• Calculate the midpoint of the line.

• Draw a perpendicular line to the line of reflection.

• Draw a parallel line to the line of reflection.

• Measure the angle of reflection.

How do you determine the position of the reflected point?

• Draw a circle around the original point.

• Measure equal distances on both sides of the line of reflection.

• Calculate the slope of the line.

• Use a compass to find the angle.