Graph the function. f(x)=2sqrt (x-1)

To graph the function $f(x)=2\sqrt {x-1}$, we need to plot the points that satisfy the equation and connect them to form a curve.<br /><br />Step 1: Identify the domain of the function.<br />The domain of the function is the set of all real numbers for which the expression under the square root is non-negative. In this case, the expression under the square root is $(x-1)$, so the domain is $x \geq 1$.<br /><br />Step 2: Choose some values of $x$ within the domain and calculate the corresponding values of $f(x)$.<br />Let's choose $x = 1$, $x = 2$, $x = 3$, and $x = 4$ as some sample values.<br /><br />For $x = 1$:<br />$f(1) = 2\sqrt{1-1} = 2\sqrt{0} = 0$<br /><br />For $x = 2$:<br />$f(2) = 2\sqrt{2-1} = 2\sqrt{1} = 2$<br /><br />For $x = 3$:<br />$f(3) = 2\sqrt{3-1} = 2\sqrt{2} \approx 2.83$<br /><br />For $x = 4$:<br />$f(4) = 2\sqrt{4-1} = 2\sqrt{3} \approx 3.46$<br /><br />Step 3: Plot the points on a coordinate plane.<br />Plot the points $(1, 0)$, $(2, 2)$, $(3, 2.83)$, and $(4, 3.46)$ on the coordinate plane.<br /><br />Step 4: Connect the points to form a curve.<br />Connect the plotted points with a smooth curve to represent the graph of the function $f(x)=2\sqrt {x-1}$.<br /><br />The final answer is the graph of the function $f(x)=2\sqrt {x-1}$.