AnswersAlgebraic ReasoningExponential and Logarithmic Functions — TestQuestion 17
17
QuizMultiple Choice

Exponential and Logarithmic Functions — Test

Question 17 • Algebraic Reasoning

Which tables could be used to verify that the functions they represent are inverses of each other? Choose two correct answers.

Answer
A
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 14'; Column 3, 'negative 10'; Column 4, 'negative 6'; Column 5, '0'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, 'negative 4'; Column 3, 'negative 2'; Column 4, '0'; Column 5, '3'; Column 6, '5'
B
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 14'; Column 3, 'negative 10'; Column 4, 'negative 6'; Column 5, '0'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, '4'; Column 3, '2'; Column 4, '0'; Column 5, 'negative 3'; Column 6, 'negative 5'
C
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '2'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, 'negative 4'; Column 3, '0'; Column 4, '6'; Column 5, '10'; Column 6, '14'
D
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '3'; Column 6, '9' Row 2: Column 1, 'y'; Column 2, 'negative 14'; Column 3, 'negative 10'; Column 4, 'negative 6'; Column 5, '0'; Column 6, '4'
E
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '2'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, '4'; Column 3, '0'; Column 4, 'negative 6'; Column 5, 'negative 10'; Column 6, 'negative 14'

Explanation

Two functions are inverses when each input-output pair in one table appears with its coordinates swapped in the other. In B, for example, the pair (−14, 4) is matched by (4, −14) in E, and (−10, 2) is matched by (2, −10). The same swap works for every pair in the tables, so B and E represent inverse functions.

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