Chapter 4.3, Problem 3P

To determine

To find: the rule for the function represented by the ordered pairs $\left(1,1\right),\left(2,4\right),\left(3,9\right),\left(4,16\right)$ and $\left(5,25\right)$

Answer to Problem 3P

  $y=x^2$

Explanation of Solution

Given information: The ordered pairs are $\left(1,1\right),\left(2,4\right),\left(3,9\right),\left(4,16\right)$ and $\left(5,25\right)$

Solution:

Let x be the independent variable and y be the dependent variable.

The x takes the values 1,2,3,4 and 5, and corresponding values of y are 1, 4,9,16 and 25 respectively.

Notice that

  $\begin{array}{l}1=1^2\\ 4=2^2\\ 9=3^2\\ 16=4^2\\ 25=5^2\end{array}$

Thus, the function rule represented by the ordered pairs is

  $y=x^2$