Question

Which piecewise relation defines a function?

a) y = x², x > -2
b) y = -3x, x < -2
c) y = 2x, x ≤ 4
d) y = 2x, x ≥ 1

Answer 1

Option d) y = 2x, x ≥ 1 defines a function because it satisfies the criteria of a function by having a unique y-value for every x-value.

Step-by-step explanation:

The piecewise relation that defines a function is option d) y = 2x, x ≥ 1.

A function must pass the vertical line test, which means that each x-value must be associated with only one y-value. In options a) and c), the values of x are not uniquely associated with y. In option b), the graph of y = x² fails the vertical line test because for every x value, there are two possible y-values.

Option d) satisfies the criteria of a function because for every value of x greater than or equal to 1, there is exactly one corresponding value of y.