Q46. - Algebra 1

Question

The table for the value of x and y given in below.

1. Write a sentence to describe the relationship between x and y in the table.
2. Write an equation that represents the data in the table.
3. Graph each ordered pair and draw the function. Describe the graph as discrete or continuous.

Step-by-Step Solution

Answer

1. The sentence is “The square of x plus 1 is equal to y”.
2. The equation is $x^2+1=y$.
3. The graph is continuous.

Part a. Step 1. Given information.

The following table is:

Part a. Step 2. Make the sentence.

If the value of x is 2, then value of y is 5.

Take the square of value of x, that is $2^2$ and add the number 1. Then get the value of y, that is 5.

Part a. Step 3. Conclusion.

The sentence for the relationship between x and y is:

 

The square of x plus 1 is equal to y.

Part b. Step 1. Given information.

The following table is:

Part b. Step 2. Make the relation.

Since,

$$\begin{gathered} 2^2+1=5 \\ {3}^2+1=10 \\ {4}^2+1=17 \\ {5}^2+1=26 \\ {6}^2+1=37 \end{gathered}$$

So, the variable x and y such that:

$x^2+1=y$

Part b. Step 3. Conclusion.

The equation for the relationship between x and y is:

$x^2+1=y$

Part c. Step 1. Given information.

The following table is:

Part c. Step 2. Make the graph.

Sketch the graph of the given data in below.

Part c. Step 3. Conclusion.

The graph is continuous.