Question

how would you draw a machine diagram for the function: f(x)=the square root of x-1

Answer 1

We want to draw a machine diagram for the function;

$f(x)\text{ = }\sqrt{x-1}$

For the machine, x enters as the input to the machine and the machine produces f(x) as its output.

For this case, according to the equation the function applies a square root operation to the value of input decreased by 1.

Lets get the Output of the machine at x = 2, x=5, x=10 and x = 17.

$\begin{gathered} at\text{ x=2} \\ f(x)\text{ = f(2) = }\sqrt{2-1}=\sqrt{1}=\text{ 1} \end{gathered}$$\begin{gathered} at\text{ x=5} \\ f(5)\text{ =}\sqrt{5-1}=\sqrt{4}=2 \\ \\ atx=10^{\square} \\ f(10)\text{ =}\sqrt{10-1}=\sqrt{9}=3 \\ \\ at\text{ x=17} \\ f(17)\text{ =}\sqrt{17-1}=\sqrt{16}=4 \end{gathered}$