Graphing Logarithmic Functions — Quiz

Question 16 • Algebraic Reasoning

Which table represents the graph of a logarithmic function in the form y is equal to the log base b of x when b is greater than 1 ?

Answer

Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 1 point 9'; Column 2, 'negative 2 point 0 9 6' Row 3: Column 1, 'negative 1 point 7 5'; Column 2, 'negative 1 point 2 6 2' Row 4: Column 1, 'negative 1 point 5'; Column 2, 'negative point 6 3 0 9' Row 5: Column 1, 'negative 1'; Column 2, '0' Row 6: Column 1, '2'; Column 2, 'point 6 3 0 9'

Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '9 eighths'; Column 2, '3' Row 3: Column 1, '1 point 2 5'; Column 2, '2' Row 4: Column 1, '1 point 5'; Column 2, '1' Row 5: Column 1, '1 point 7 5'; Column 2, 'point 4 1 5' Row 6: Column 1, '2'; Column 2, '0'

Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1 eighth'; Column 2, '0' Row 3: Column 1, '1 fourth'; Column 2, '1' Row 4: Column 1, '1 half'; Column 2, '2' Row 5: Column 1, '1'; Column 2, '3' Row 6: Column 1, '2'; Column 2, '4'

Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1 eighth'; Column 2, 'negative 3' Row 3: Column 1, '1 fourth'; Column 2, 'negative 2' Row 4: Column 1, '1 half'; Column 2, 'negative 1' Row 5: Column 1, '1'; Column 2, '0' Row 6: Column 1, '2'; Column 2, '1'

Explanation

For y = log_b(x), the function is increasing when b > 1, and log_b(1) = 0. In choice D, the table includes (1, 0) and (2, 1), so the base is 2; the other values also fit, since log₂(1/2) = −1, log₂(1/4) = −2, and log₂(1/8) = −3. Therefore, the table for the logarithmic function with base greater than 1 is choice D.

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