Carter is collecting data on the number of giraffes in Africa over time.

Question

Carter has created a scatter plot that shows the relationship between the number of giraffes g and time x.

She thinks the data might show that g is a quadratic function of x.

Which graph will show a linear relationship if Carter's data is indeed quadratic?

Answer choices are:

 

A. g vs. log(x)

B. g vs. √x

C. √g vs. x

D. g vs. x

Answer 1

The "best" answer appears to be D, since √g vs. x could be linear, if the quadratic function for the relationship between x and g is g=x².  (In that case √g = x.)  So it will be linear if a=1, b=0, and c=0 for a quadratic function in the ax² + bx + c format.

 

But √g vs. x would not be linear for other possible quadratic functions.  (Other values of a, b, and c.)  So D would be the answer IF the question was "which graph MIGHT show a linear relationship" instead of which graph "WILL show a linear relationship."

 

None of the other choices would be linear.