Functions and Their Inverses

The video tutorial guides students through using Desmos to graph functions and their inverses, emphasizing the visual and algebraic relationships between them. It highlights the symmetry across the line y = x and explains how to identify and graph inverse functions. The tutorial also covers the concept of relations and their inverses, using examples to illustrate these mathematical ideas.

What tool does the teacher ask students to use for graphing functions and their inverses?

• Wolfram Alpha

• Desmos

• GeoGebra

• Graphing Calculator

What is the line of symmetry for a function and its inverse?

• x = y

• y = x

• x = 0

• y = 0

How can you algebraically find the inverse of a function?

• Divide by 2

• Add 1 to both sides

• Multiply by -1

• Swap x and y, then solve for y

What happens to a point on a function when finding its inverse?

• It moves to the origin

• It reflects across y = x

• It doubles in value

• It remains unchanged

Which point on a function remains unchanged when finding its inverse?

• The origin

• Any point on y = x

• The maximum point

• The minimum point

What happens to the coordinates of a point (a, b) when finding the inverse of a function?

• They remain (a, b)

• They become (a, -b)

• They become (b, a)

• They become (-a, b)

What test is used to determine if a graph represents a function?

• Horizontal Line Test

• Slope Test

• Vertical Line Test

• Symmetry Test

What does the vertical line test check for?

• If a graph is decreasing

• If a graph is increasing

• If a graph is a function

• If a graph is symmetrical

What is the center of the circle described by x^2 + (y-2)^2 = 4?

• (2, 2)

• (0, 0)

• (2, 0)

• (0, 2)

What is the radius of the circle described by x^2 + (y-2)^2 = 4?

• 4

• 1

• 3

• 2