Question

Which table represents a linear function? ( all x tables adre "1,2,3,4" i.e. A. x 1,2,3,4. y 1/2, 1, 1 1/2, 2. B. y 1, 1/2, 1/3, 1/4. C. y 7, 9, 13, 21. D. y 0, 6, 16, 30

Answer 1

Explanation:

Based on the given tables for x = 1, 2, 3, and 4:

A. x: 1, 2, 3, 4. y: 1/2, 1, 1 1/2, 2

B. x: 1, 2, 3, 4. y: 1, 1/2, 1/3, 1/4

C. x: 1, 2, 3, 4. y: 7, 9, 13, 21

D. x: 1, 2, 3, 4. y: 0, 6, 16, 30

A linear function has a constant rate of change (slope). Let's calculate the differences in y-values for each table:

A. 1 - 1/2 = 1/2, 1 1/2 - 1 = 1/2, 2 - 1 1/2 = 1/2 (constant differences)

B. 1 - 1/2 = 1/2, 1/2 - 1/3 = 1/6, 1/3 - 1/4 = 1/12 (not constant)

C. 9 - 7 = 2, 13 - 9 = 4, 21 - 13 = 8 (not constant)

D. 6 - 0 = 6, 16 - 6 = 10, 30 - 16 = 14 (not constant)

Table A represents a linear function, as the differences in the y-values are constant (1/2).