Chapter 1.5, Problem 3BGP

a.

To determine

To write: A sentence describing the relation between $x$ and $y$ in the given table.

Answer to Problem 3BGP

Each $y$ is the sum of square of the corresponding $x$ and 1.

Explanation of Solution

Given Information: A table showing the values of $x$ and $y$ is given.

From the table,

  $5=2^2+1,10=3^2+1,17=4^2+1,26=5^2+1,37=6^2+1$

i.e., each $y$ is the sum of square of the corresponding $x$ value and 1.

Thus, each $y$ is the sum of square of the corresponding $x$ and 1.

b.

To determine

To write: An equation that represents the data in the table.

Answer to Problem 3BGP

The equation is $y=x^2+1$ .

Explanation of Solution

Given Information: A table showing the values of $x$ and $y$ is given.

  $5=2^2+1,10=3^2+1,17=4^2+1,26=5^2+1,37=6^2+1$ .

i.e., each $y$ is the sum of square of the corresponding $x$ and 1.

Examining the pattern of the relation, it can be established that the equation is $y=x^2+1$ .

Thus, the equation is $y=x^2+1$ .

c.

To determine

To graph: Each ordered pair and draw the function and then to further describe the graph as discrete or continuous.

Answer to Problem 3BGP

The graph is continuous.

Explanation of Solution

Given Information: A table showing the values of $x$ and $y$ is given.

Graph:

  

Graphing each ordered pair, analyzing the equation $y=x^2+1$ and graphing other points, a $U$ -shaped graph is obtained. As the above graph can be drawn without lifting the pen/pencil, a continuous shape is formed, points are not separated (without connection), so, the graph is continuous.

Thus, the graph is continuous.