The following post shows an example of how to evaluate functions. We have an input, and we would like to get the corresponding output:
Substitute Input → Solve Function → Get Output
Finding the output of a given input is straightforward. All we have to do is (1) substitute the independent variable in the expression with the inputs, (2) evaluate the expression, and (3) get the output. This process is often called "evaluation."
Single Input
Given the function between the area of a circle \(A\) and radius \(r\): \(A(r)=\pi{r^2}\), let's find the output with radius 1 and 2.
In this example, the independent variable is radius \(r\). The inputs are 1 and 2. We first substitute the input to \(r\):
\(A(1)=\pi\times{1^2}\)
\(A(2)=\pi\times{2^2}\)
Afterward, we evaluate the expressions:
\(A(1)=\pi\times{1}\)
\(A(2)=\pi\times{4}\)
Finally, we get the final answer:
\(A(1)=\pi\)
\(A(2)=4\pi\)
Multiple Inputs
Given the function of the volume of a right cylinder in terms of its circular base area \(A\) and height \(h\): \(V(A,h)=Ah\), let's find the volume with a base of 3 square units and a height of 2 units.
This function has multiple independent variables: \(A\) and \(h\). The inputs are 3 and 2, respectively. We substitute the inputs to \(A\) and \(h\):
\(V(3,2)=3\times2\)
Afterward, we evaluate the expression:
\(V(3,2)=6\)
Finally, we get the final answer:
\(V(3,2)=6\)
Summary
Evaluating functions involves the following steps: (1) substitute the independent variable in the expression with the inputs, (2) evaluate the expression, and (3) get the output.
