Which of these functions is a linear function?

B.

For A. f(x)= 2x², That's obviously a quadratic.

For C, f(x)= 1 / 2x, the x is in the denominator of the fraction, not the numerator, so it's not a linear function.

For D, f(x)= - 1/ 2(x-2), the x is in the denominator of the fraction, not the numerator, so it's not a linear function neither.

So the answer is B

Mmm, Some of your answers I agree with Max but some are open to interpretation.

Which of these functions is a linear function?

a. f(x) = 2x²     yes defintely NOT a lnear graph.

 Linear graphs cannot have x raised to any power (except 1 which is invisable) 

b. f(x) = (1 / 2)²x  =   $(\frac{1}{2})^2x = \frac{1}{4}x=0.25x \qquad \mbox{YES this is definitely a LINEAR equation}$

c. f(x) = 1 / 2x 

If you mean f(x)=1/(2x) then it is not linear becasue x cannot be on the bottom.

If you mean  (1/2)*x then it IS LINEAR

d. f(x) = - 1 / 2(x - 2)

If you mean$f(x)=\frac{-1}{2(x-2)}$

                       then it is NOT linear becasue x cannot be on the bottom.

If you mean  $f(x)=\frac{-1}{2}(x-2)$

                     then it IS LINEAR