Inverse Variation Concepts and Properties

The video tutorial explains inverse variation, highlighting two forms of the equation. It demonstrates how to plot points that form curves and explores the concept of symmetry with negative values. The tutorial also covers how sign changes affect the position of points in different quadrants, ultimately illustrating the characteristics of inverse functions.

What is the basic form of an inverse variation equation?

• x / y = k

• x * y = k

• x - y = k

• x + y = k

In an inverse variation, if x is 1 and y is 6, what is the constant k?

• 6

• 5

• 7

• 8

If x is 2 and y is 3 in an inverse variation, what is the value of k?

• 7

• 6

• 8

• 5

In an inverse variation, if x is 6 and y is 1, what is the constant k?

• 8

• 6

• 5

• 7

What shape is formed when plotting points of an inverse variation?

• A straight line

• A parabola

• A circle

• A curve

What happens to the curve when x and y values are plotted?

• It forms a curve

• It forms a straight line

• It forms a circle

• It forms a triangle

What happens to the curve when the signs of x and y are changed?

• A second curve appears

• It remains the same

• It becomes a straight line

• It disappears

What is the result of multiplying negative x and y values in an inverse variation?

• Undefined

• Zero

• A negative product

• A positive product

What is the symmetry of the inverse variation curve about the origin?

• No symmetry

• Symmetric about the x-axis

• Symmetric about the y-axis

• Symmetric about the origin

Which quadrant is associated with positive x and negative y values?

• Quadrant 4

• Quadrant 3

• Quadrant 2

• Quadrant 1