Question

Given that D(x) = 2x, select all of the following that are true statements.

D(x) is a function.
x is the dependent variable.
D(6) = 3
D(x) is a direct variation.
D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4).

Answer 1

Explanation:

D(x) is a function. TRUE. It is a function of x.

x is the dependent variable. FALSE. x is the independent variable because the function is expressed in terms of the independent variable.

D(6) = 3. FALSE. D(6) = 2(6) = 12. D(6) should be equal to 12.

D(x) is a direct variation. TRUE. This holds true to the definition of direct variation where one variable is related to the other variable at the same constant multple. In this case, it is 2.

D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). TRUE. If you replace x with the first coordinate, the function would be equal to the corresponding second coordinate.

Answer 2

D(x) is a function. TRUE. It is a function of x.

x is the dependent variable. FALSE. x is the independent variable because the function is expressed in terms of the independent variable.

D(6) = 3. FALSE. D(6) = 2(6) = 12. D(6) should be equal to 12.

D(x) is a direct variation. TRUE. This holds true to the definition of direct variation where one variable is related to the other variable at the same constant multple. In this case, it is 2.

D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). TRUE. If you replace x with the first coordinate, the function would be equal to the corresponding second coordinate.