Answer:
D(x) is a function
D(x) is a direct variation
D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem
[tex]D(x)=2x[/tex]
D(x) is a direct variation (linear function)
The variable x is the independent variable or input value
The variable D(x) is the dependent variable or output value
Verify each statement
case 1) D(x) is a function
The statement is true
see the explanation
case 2) x is the dependent variable
The statement is false
The variable x is the independent variable or input value
case 3) D(x) is a direct variation
The statement is true
see the explanation
case 4) D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)
The statement is true
Because
For x=5
substitute in the linear equation
[tex]D(x)=2(5)=10[/tex] ---> is ok
For x=6
substitute in the linear equation
[tex]D(x)=2(6)=12[/tex] ---> is ok
For x=-2
substitute in the linear equation
[tex]D(x)=2(-2)=-4[/tex] ---> is ok
