Look at the functions in the table below.

Is there a property or feature that is shared by two functions in a row but not the third? If so, we can say that the third function is the odd one out.

Find a reason why each function in the table could be the odd one out in its row.

\(y=\sin x^2\) \(y=\ln{x^2}\) \(y=\tan x (\sec^2 x-1)\)
\(y=9x^2-6x+1\) \(y=\ln{3x}\) \(y=\sqrt{3x-1}\)
\(y=e^{5x}\) \(y=\dfrac{1}{x^2+4x+4}\) \(y=e^{x+4}\)
  • What features does the graph of \(y\) as a function of \(x\) have?

  • Where is \(y\) an increasing or decreasing function?

  • What is \(\dfrac{dy}{dx}\)?

  • What functions is \(y\) composed from?

You may find it helpful to plot these functions on Desmos, but try to think about the functions and their gradient functions first.

Can you also find an odd one out within each column?