Reflection and Inverse Functions

The video tutorial explains how to reflect a line across the line y=x. It starts by introducing the concept of reflection and how to interchange x and y coordinates to find new points. The tutorial then demonstrates how to calculate the slope of the new line and derive its equation. It also covers solving the equation for y and visualizing the reflection on a graph, showing how the original and reflected lines are mirror images across y=x.

What is the initial equation of the line before reflection?

• y = 3x + 2

• y = x + 3

• y = 2x + 3

• y = 3x - 2

What is the line across which the reflection is performed?

• x = y

• y = 2x

• y = x

• x = 2y

What happens to the coordinates of points when they are reflected across y = x?

• They are halved

• They remain the same

• They are doubled

• x and y coordinates are interchanged

What is the slope of the new line after reflection?

• -1/3

• 3

• -3

• 1/3

Which form is used to plug in a point to find the equation of the line?

• Slope-intercept form

• Standard form

• Intercept form

• Point-slope form

What is the process called when x and y are interchanged in an equation?

• Finding the derivative

• Finding the product

• Finding the integral

• Finding the inverse

What is the equation after interchanging x and y and solving for y?

• y = (x - 2) / 3

• y = 3x + 2

• y = 2x - 3

• y = x + 2

What is the simplified form of the equation after reflection?

• y = x - 2

• y = 3x + 2

• y = 1/3x - 2/3

• y = 2x + 3

Why is the simplified equation harder to graph?

• It is not linear

• It has too many variables

• It is too complex

• It is not in y = mx + b form

What is the y-intercept of the reflected line?

• 1

• 0

• 2/3

• -2/3