Question

Machine Diagram Draw a machine diagram for the function.

$f\left(x\right)=\frac{3}{x-2}$

Short answer

A machine diagram is a diagrammatical representation of function operation on variable x to produce variable output y.

If x is in the domain of the function f, then when x enters the machine, it is accepted as an input and the machine produces an output y according to the rule of the function.

Step-by-step solution

Step 1. use the definition of functions.

A machine diagram is a diagrammatical representation of function operation on variable x to produce variable output y.

If x is in the domain of the function f, then when x enters the machine, it is accepted as an input and the machine produces an output y according to the rule of the function.

Step 2. Analyze the information given.

We are given the function, $f\left(x\right)=\frac{3}{x-2}$, observe that variable x is subtracted by 2 and difference is in numerator with 3 as denominator, thus machine diagram will be as shown:

Step 3. Evaluate the results.

We are given the function, $f\left(x\right)=\frac{3}{x-2}$, from diagram observe that variable x is subtracted by 2 and difference is put in fraction of the denominator with numerator 3, thus machine diagram is verified.