## 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 $h(x)=-\sqrt{x+1}=-f(x+1)$ is obtained by "Horizontal shifts $y=f(x+c)$ Shift the graph of $f$ to the left $c$ units. $x$ is replaced with $x+c$." and then "Reflection about the x-axis $y=-f(x)$ Reflect the graph of $f$ about the x-axis. $f(x)$ is multiplied by $-\mathrm{l}$ " So, using our table (x, f(x)) We plot the points ( $x-1,\ -f(x)$ ), moving the originals to the left and flipping them across the x-axis, Join them with a smooth curve, (red solid line on the screenshot), and we have the graph of h(x).