Final answer:
The function D(x) = 2x is indeed a function and a direct variation that matches the given set of points. However, D(6) does not equal 3, and x is the independent variable, not the dependent one.
Step-by-step explanation:
The function given is D(x) = 2x. Let's evaluate the statements one by one.
- D(x) is a function. This is true because for every input x, there is exactly one output, which is 2 times x.
- x is the dependent variable. This is false; x is the independent variable, and D(x) is the dependent variable since the output depends on the value of x.
- D(6) = 3 is false; substituting x with 6 gives D(6) = 2*6 = 12.
- D(x) is a direct variation. This is true since it is of the form y = kx, where k is a constant, and there is no constant term.
- D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). This is true because substituting those x values into the function D(x) gives the corresponding y values.