Linear vs. Nonlinear Functions — Quiz

Question 5 • Transition Mathematics for Seniors

Which of these tables represents a non-linear function?

Answer

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '17'; Column 2, 'negative 16' Row 3: Column 1, '18'; Column 2, 'negative 17' Row 4: Column 1, '19'; Column 2, 'negative 18' Row 5: Column 1, '20'; Column 2, 'negative 19'

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '17'; Column 2, '20' Row 3: Column 1, '18'; Column 2, '19' Row 4: Column 1, '19'; Column 2, '18' Row 5: Column 1, '20'; Column 2, '17'

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '17'; Column 2, 'negative 20' Row 3: Column 1, '18'; Column 2, 'negative 19' Row 4: Column 1, '19'; Column 2, 'negative 18' Row 5: Column 1, '20'; Column 2, 'negative 17'

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '17'; Column 2, '16' Row 3: Column 1, '18'; Column 2, '17' Row 4: Column 1, '19'; Column 2, '19' Row 5: Column 1, '20'; Column 2, '20'

Explanation

A function is linear when equal changes in x produce a constant change in y. In choice D, x increases by 1 each time, but y changes by +1, then +2, then +1, so the rate of change is not constant. Therefore, the table for choice D, with y-values 16, 17, 19, and 20, represents a non-linear function.

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