Question

Which equations represent a relationship where y is a nonlinear function of x? Select all that apply.

O y =∣x∣ + 1
O y = √4x
O X = -6 y
O X - 5 y = 2
O y = 2+1/x
O y = 1/4x +1/16

Answer 1

The equations y = |x| + 1, y = √4x, and y = 2 + 1/x represent nonlinear relationships between x and y. They cannot be expressed as y = mx + b and their graphs are not straight lines, indicating nonlinearity.

Step-by-step explanation:

To determine which equations represent a nonlinear function of x, we assess whether each equation can be expressed in the form y = mx + b, which represents a linear equation. Nonlinear equations have graphs that are not straight lines and include curves such as parabolas, hyperbolas, and circles.

• y = |x| + 1 represents a nonlinear function because the absolute value of x leads to a V-shaped graph.
• y = √4x is nonlinear because it represents the square root function, which produces a curved graph.
• x = -6y is linear because it can be rearranged to y = -1/6x.
• x - 5y = 2 is linear, as it can be rearranged to y = 1/5x - 2/5.
• y = 2 + 1/x is nonlinear, showing an inverse relationship between x and y, which results in a hyperbola when graphed.
• y = 1/4x + 1/16 is linear, as it is in the form y = mx + b with m = 1/4 and b = 1/16.

The three equations that represent a nonlinear relationship between x and y are y = |x| + 1, y = √4x, and y = 2 + 1/x.