Question

Make an input-output table for the function. Use 1, 1.5, 3, 4.5, and 6 as the domain. $$ y=x^{2}-0.5 $$

Short answer

The table values are: for x = 1, y = 0.5; for x = 1.5, y = 1.75; for x = 3, y = 8.5; for x = 4.5, y = 19.75; for x = 6, y = 35.5.

Step-by-step solution

Understand the function

The given function is \(y=x^{2}-0.5\). For a set of x-values, you should calculate the corresponding y-values. This will be done by substituting each x-value into the function.

Substitute x=1

The x-value is 1. Substituting it into the function will give: \(y=1^{2}-0.5=1-0.5=0.5\).

Substitute x=1.5

The x-value is 1.5. Substituting it into the function will give: \(y=1.5^{2}-0.5=2.25-0.5=1.75\).

Substitute x=3

The x-value is 3. Substituting it into the function will give: \(y=3^{2}-0.5=9-0.5=8.5\).

Substitute x=4.5

The x-value is 4.5. Substituting it into the function will give: \(y=4.5^{2}-0.5=20.25-0.5=19.75\).

Substitute x=6

The x-value is 6. Substituting it into the function will give: \(y=6^{2}-0.5=36-0.5=35.5\).

Summarize in a table

Now, put all your x and y values in a table. So, your Input-Output Table would look like: \n| x | y |\n|---|---|\n| 1 | 0.5 |\n| 1.5 | 1.75 |\n| 3 | 8.5 |\n| 4.5 | 19.75 |\n| 6 | 35.5 |