Chapter 3.3, Problem 27MS

Is a square a one-to-one correspondence? (H) Sketch a graph of the function $y=x^2.$

Using your graph, determine if this function provides a one-to-one correspondence between the real numbers on the x-axis and the real numb ers on the y-axis. If it does give a one-to-one correspondence between the numbers on the two axes, justify your answer using your graph. If not, use your graph to explain why that function is not a one-to-one correspondence. In particular, does every number on the x-axis correspond to exactly one number on the y-axis? Does every number on the y-axis correspond to exactly one number on the x-axis?