Question

The function f(x) is defined as f(x) = One-third(6)x. Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis? A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries 12, 2, one-third, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries 12, 2, 0, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12.

Answer 1

The correct table for reflection of f(x) across the x-axis will have g(x) values that are the negatives of the corresponding f(x) values.

Step-by-step explanation:

The student's question involves reflection of a function f(x) across the x-axis to obtain a new function g(x). A reflection across the x-axis will change the sign of the y-values (or f(x) values) while keeping the x-values the same. Thus, if f(x) = One-third(6)x, the reflected function g(x) will have its y-values (the outputs) as the negatives of what f(x) produces for corresponding x-values. Therefore, the correct table that can be used to graph g(x) would list the same x-values as f(x), with each y-value being the opposite in sign to the f(x) value.

Looking at the provided options, the correct choice is the table where all of the g(x) entries are the negatives of f(x) entries. Hence, the correct reflection of f(x) across the x-axis is g(x) with entries -StartFraction 1 Over 108 EndFraction, -One-eighteenth, -one-third, -2, -12.