Question

Assuming a>0, which of the following statements about the function f(x)=a(b)x are TRUE?

A) f(x) is directly proportional to
B) f(x) is inversely proportional to
C) f(x) is not affected by the value of
D) f(x) is linear.
E) f(x) is a quadratic function.

Answer 1

The function ( f(x) = a(b)x ) signifies direct proportionality, with ( a ) as a positive constant. In direct proportionality, ( f(x) ) varies directly with ( x ).The correct answer is A) f(x) is directly proportional to.

Step-by-step explanation:

The function ( f(x) = a(b)x ) is said to be directly proportional when changes in the independent variable (( x )) lead to proportional changes in the dependent variable (( f(x) )). This property aligns with the given function, ( f(x) = a(b)x ), where the coefficient ( a ) represents a positive constant. In direct proportionality, as ( x ) increases, ( f(x) ) also increases by a factor of ( a(b) ), maintaining a constant ratio.

In mathematical terms, direct proportionality is expressed as ( f(x) = kx ), where ( k ) is a constant. In the given function ( f(x) = a(b)x ), the presence of the positive constant ( a ) implies direct proportionality. If ( a ) were negative, it would indicate inverse proportionality. Additionally, linearity is a characteristic of direct proportionality, making option D,f(x) is linear, true in this context.

Therefore, the correct choice is A) f(x) is directly proportional to, as the function exhibits direct proportionality between ( f(x) ) and ( x ) due to the positive constant ( a ).