Figure

Use transformations to graph the function $f( x) =\sqrt{1-x}+2$ .

We graph $f$ in steps:

Observe that

$f$ is basically a square root function, so we begin by graphing

$y=\sqrt{x}$ . See Figure 47(a).

Now we replace the argument

$x$ with

$x+1$ to obtain

$y=\sqrt{x+1},$ which shifts the graph of

$y=\sqrt{x}$ horizontally to the left

$1$ unit, as shown in Figure 47(b).

Then we replace

$x$ with

$-x$ to obtain

$y=\sqrt{-x+1}=\sqrt{1-x},$ which reflects the graph about the

$y$ -axis. See Figure 47(c).

Finally, we add

$2$ to each

$y$ -coordinate, which shifts the graph vertically up 2 units, and results in the graph of

$f( x) = \sqrt{1-x}+2$ shown in Figure 47(d).