13) y=4sqrt (x-2)-1 A y square square square square

To graph the function $y=4\sqrt{x-2}-1$, we need to follow these steps:<br /><br />Step 1: Identify the domain of the function.<br />The domain of the function is the set of all possible values of x for which the function is defined. In this case, the function is defined for all x values greater than or equal to 2, since the square root of a negative number is not a real number. Therefore, the domain of the function is $x \geq 2$.<br /><br />Step 2: Plot points on the graph.<br />To plot points on the graph, we can choose some x values within the domain and calculate the corresponding y values using the given function. Let's choose x = 2, x = 3, x = 4, and x = 5 as our sample points.<br /><br />When x = 2:<br />$y = 4\sqrt{2-2} - 1 = 4\sqrt{0} - 1 = 0 - 1 = -1$<br /><br />When x = 3:<br />$y = 4\sqrt{3-2} - 1 = 4\sqrt{1} - 1 = 4(1) - 1 = 3$<br /><br />When x = 4:<br />$y = 4\sqrt{4-2} - 1 = 4\sqrt{2} - 1 = 4(\sqrt{2}) - 1 = 4\sqrt{2} - 1$<br /><br />When x = 5:<br />$y = 4\sqrt{5-2} - 1 = 4\sqrt{3} - 1 = 4(\sqrt{3}) - 1 = 4\sqrt{3} - 1$<br /><br />Step 3: Connect the points.<br />Now that we have plotted the points, we can connect them to form the graph of the function. The graph will be a curve that starts at the point (2, -1) and increases as x increases.<br /><br />Answer: The graph of the function $y=4\sqrt{x-2}-1$ is a curve that starts at the point (2, -1) and increases as x increases.