Question

Make an input-output table for the function \(A=8+2.5 t\) when \(t=2,3,4,5,\) and \(6 .\) Describe the domain and the range of the function whose values are shown in the table.

Short answer

The input-output table of the function will be: for \(t=2\), \(A=13\); \(t=3\), \(A=15.5\); for \(t=4\), \(A=18\); for \(t=5\), \(A=20.5\); for \(t=6\), \(A=23\). The domain of the function is \(t = 2, 3, 4, 5, 6\) and the range is \(A = 13, 15.5, 18, 20.5, 23\).

Step-by-step solution

Create an Input-Output Table

Substitute the given values for \(t\) into the function \(A=8+2.5 t\) to find the corresponding value of \(A\).For \(t=2\), compute \(A\) as: \(A=8+2.5*2=13\)For \(t=3\), compute \(A\) as: \(A=8+2.5*3=15.5\)For \(t=4\), compute \(A\) as: \(A=8+2.5*4=18\)For \(t=5\), compute \(A\) as: \(A=8+2.5*5=20.5\)For \(t=6\), compute \(A\) as: \(A=8+2.5*6=23\)

Determine the Domain

The domain of a function is the set of all possible input values (here, \(t\) values). In this case, the domain is \(t = 2, 3, 4, 5, 6\)

Identify the Range of the Function

The range is the set of all possible outputs of the function, in this case, corresponding \(A\) values. For the given values of \(t = 2, 3, 4, 5, 6\), the calculated range is \(A = 13, 15.5, 18, 20.5, 23\)