Question

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

Short answer

The input-output table for the function \(y=1.5+x^{2}\) is: x = [1, 1.5, 3, 4.5, 6] y = [2.5, 3.75, 10.5, 21.75, 37.5].

Step-by-step solution

Identify function

Identify the formula given for the function which is \(y=1.5+x^{2}\). This function tells us how to get an output (y) for every input (x).

List the given inputs

List the given values of x which are 1, 1.5, 3, 4.5, and 6.

Compute the output for each input

Substitute each x value into the function to solve for y. That means, calculate \(y=1.5+x^{2}\) for each x in the list.

Calculate y when x=1

Substitute x=1 into the function to get \(y=1.5+1^{2}=1.5+1=2.5\). So when x=1, y=2.5.

Calculate y when x=1.5

Substitute x=1.5 into the function to get \(y=1.5+(1.5)^{2}=1.5+2.25=3.75\). So when x=1.5, y=3.75.

Calculate y when x=3

Substitute x=3 into the function to get \(y=1.5+3^{2}=1.5+9=10.5\). So when x=3, y=10.5.

Calculate y when x=4.5

Substitute x=4.5 into the function to get \(y=1.5+(4.5)^{2}=1.5+20.25=21.75\). So when x=4.5, y=21.75.

Calculate y when x=6

Substitute x=6 into the function to get \(y=1.5+6^{2}=1.5+36=37.5\). So when x=6, y=37.5.

Write out the input-output table

Finally, to make an input-output table for the function, write the corresponding x (input) and y (output) values in tabular form: x = [1, 1.5, 3, 4.5, 6] y = [2.5, 3.75, 10.5, 21.75, 37.5].