Inverse Variation Concepts and Problems-Nest

What mathematical relationship describes inverse variation between two variables, y and x, with a constant k?

• y = kx

• y = k + x

• y = k/x

• y = k - x

What is the relationship between the product of the two variables, x and y, in an inverse variation?

• The product x*y is always increasing.

• The product x*y is always decreasing.

• The product x*y is a constant.

• The product x*y is always zero.

In an inverse variation where the constant of variation (k) is positive, what is the general trend between the variables x and y?

• As x increases, y also increases.

• As x decreases, y also decreases.

• As x increases, y decreases.

• Both x and y remain constant.

If y varies inversely as x, and y = 2 when x = 6, what is the value of the constant of variation (k)?

• 3

• 8

• 12

• 24

Based on the values y = 2 and x = 6 for an inverse variation, what is the specific equation relating y and x?

• y = 6/x

• y = 2/x

• y = 12/x

• y = x/12

For the inverse variation equation y = 12/x, what is the value of y when x = -6?

• -2

• -3

• -4

• -6

For the inverse variation equation y = 12/x, what is the value of y when x = -2?

• -2

• -3

• -4

• -6

For the inverse variation equation y = 12/x, what is the value of y when x = 4?

• 2

• 3

• 4

• 6

In the graph of an inverse variation y = k/x, which line(s) act as asymptotes, meaning the curve approaches but never touches them?

• Only the x-axis

• Only the y-axis

• Both the x-axis and the y-axis

• Neither the x-axis nor the y-axis

What is the graphical representation of an inverse variation relationship?

• A straight line

• A parabola

• A hyperbola

• An ellipse