Warm-up

Can you think of examples of the following?

  • a number less than \(3\) whose square is greater than \(9\)

  • a number whose cube is larger than \(27\)

  • a number whose reciprocal is smaller than \(\dfrac{1}{3}\)

One way to think about questions like these is to think about functions. Which functions are involved here and what do their graphs look like?