The following table lists some –values for the function
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
The following table lists some x–values for the function y=x1, but only two corresponding y–values have been filled in.
(a)
| x | −5 | −1 | −51 | 51 | 1 | 5 |
|-----|-----|-----|-------|-------|-----|-----|
| y | ? | ? | ? | 5 | 1 | ? |
Fill every blank so that the table represents the curve y=x1.
(b) (ii) From the completed table, decide whether the curve meets either the x–axis or the y–axis at any point. Justify your answer with reference to the values in the table.
(c) (iii) Explain briefly why the values you obtained suggest that the axes act as boundaries which the curve approaches but never touches.