Linear vs. Nonlinear Functions — Quiz

Question 4 • Transition Mathematics for Seniors

Which of these tables represents a linear function?

Answer

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '3'; Column 2, '2' Row 3: Column 1, '4'; Column 2, '4' Row 4: Column 1, '5'; Column 2, '5' Row 5: Column 1, '6'; Column 2, '6'

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '3'; Column 2, '7' Row 3: Column 1, '4'; Column 2, '6' Row 4: Column 1, '5'; Column 2, '5' Row 5: Column 1, '6'; Column 2, '3'

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '3'; Column 2, '3' Row 3: Column 1, '4'; Column 2, '4' Row 4: Column 1, '5'; Column 2, '6' Row 5: Column 1, '6'; Column 2, '7'

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '3'; Column 2, '6' Row 3: Column 1, '4'; Column 2, '5' Row 4: Column 1, '5'; Column 2, '4' Row 5: Column 1, '6'; Column 2, '3'

Explanation

A table represents a linear function when equal changes in x produce equal changes in y. In choice D, x increases by 1 each time, and y changes from 6 to 5 to 4 to 3, decreasing by 1 each time. The rate of change is constant, so choice D, with y-values 6, 5, 4, and 3, represents a linear function.

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