AnswersAlgebraic ReasoningN/A — ExamQuestion 21
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N/A — Exam

Question 21 • Algebraic Reasoning

The tables show two functions evaluated for the given values of x x negative 8 negative 4 4 8 f of x negative 6 negative 2 6 10 x negative 8 negative 4 4 8 g of x 54 10 18 70 Which table shows the values of the combined function determined by dividing g of x by f of x ?

Answer
A
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'g of x over f of x' Row 2: Column 1, 'negative 8'; Column 2, '1 ninth' Row 3: Column 1, 'negative 4'; Column 2, '1 fifth' Row 4: Column 1, '4'; Column 2, 'negative 1 third' Row 5: Column 1, '8'; Column 2, 'negative 1 seventh'
B
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'g of x over f of x' Row 2: Column 1, 'negative 8'; Column 2, 'negative 9' Row 3: Column 1, 'negative 4'; Column 2, 'negative 5' Row 4: Column 1, '4'; Column 2, '3' Row 5: Column 1, '8'; Column 2, '7'
C
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'g of x over f of x' Row 2: Column 1, 'negative 8'; Column 2, 'negative 1 ninth' Row 3: Column 1, 'negative 4'; Column 2, 'negative 1 fifth' Row 4: Column 1, '4'; Column 2, '1 third' Row 5: Column 1, '8'; Column 2, '1 seventh'
D
Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'g of x over f of x' Row 2: Column 1, 'negative 8'; Column 2, '9' Row 3: Column 1, 'negative 4'; Column 2, '5' Row 4: Column 1, '4'; Column 2, 'negative 3' Row 5: Column 1, '8'; Column 2, 'negative 7'

Explanation

Divide each g(x) value by the corresponding f(x) value: 54 ÷ (−6) = −9, 10 ÷ (−2) = −5, 18 ÷ 6 = 3, and 70 ÷ 10 = 7. These results match the table with values −9, −5, 3, and 7, which is choice B.

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