## College Algebra (6th Edition) $f(x)=\sqrt{x}$ Using desmos.com, we graph f(x) (blue dashed graph) By hand, we select some values for x and make a table with x ... f(x) as columns. Each pair gives a point on the graph of f(x). (In the screenshot, the table is to the left ) Plotting the points (x,f(x)) and joining them with a smooth curve, we have the graph of f(x). Using Table 2.4, Summary of Transformations, we see that $g(x)=2\sqrt{x+2}-2=2f(x+2)-2$ is obtained by "Horizontal shifts $y=f(x+c)$ Shift the graph of $f$ to the left $c$ units." "Vertical stretching or shrinking, $y=cf(x),\ c > 1$ Multiply each y-coordinate of $y=f(x)$ by $c$, vertically stretching the graph of $f$. " and "Vertical shifts, $y=f(x)-c$ Lower the graph of $f$ by $c$ units. $c$ is subtracted from $f(x)$." So, using our table (x, f(x)) We plot the points ( $x-2,\ 2f(x)-2$ ), moving the originals to the left, double their f(x) coordinate (stretch vertically), and then shifting them down. Join them with a smooth curve, (red solid line on the screenshot), and we have the graph of g(x).