Introduction to Quadratic Functions — Quiz

Question 9 • Algebra I

Which function increases at the fastest rate between x is equal to 0 and x is equal to 8 ?

Answer

Exponential Function f of x is equal to 2 to the x th power plus 2 Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'f of x' Row 2: Column 1, '0'; Column 2, '3' Row 3: Column 1, '2'; Column 2, '6' Row 4: Column 1, '4'; Column 2, '18' Row 5: Column 1, '6'; Column 2, '66' Row 6: Column 1, '8'; Column 2, '258'

Linear Function f of x is equal to 3 x plus 2 Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'f of x' Row 2: Column 1, '0'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '8' Row 4: Column 1, '4'; Column 2, '14' Row 5: Column 1, '6'; Column 2, '20' Row 6: Column 1, '8'; Column 2, '26'

Quadratic Function f of x is equal to 2 x squared plus 2 Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'f of x' Row 2: Column 1, '0'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '10' Row 4: Column 1, '4'; Column 2, '34' Row 5: Column 1, '6'; Column 2, '74' Row 6: Column 1, '8'; Column 2, '130'

Linear Function f of x is equal to 2 x plus 2 Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'f of x' Row 2: Column 1, '0'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '6' Row 4: Column 1, '4'; Column 2, '10' Row 5: Column 1, '6'; Column 2, '14' Row 6: Column 1, '8'; Column 2, '18'

Explanation

Compare each function’s average rate of change from x = 0 to x = 8 by dividing the change in output by 8. For choice B, the output rises from 3 to 258, so its rate is (258 − 3) ÷ 8 = 31.875, which is greater than the rates for the other choices.

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