Question

# Sketch a graph of the function. Use transformations of functions whenever possible. f(x)=1-sqrt{x}+2

Transformations of functions
Sketch a graph of the function. Use transformations of functions whenever possible. $$\displaystyle{f{{\left({x}\right)}}}={1}-\sqrt{{{x}}}+{2}$$

2021-02-13

Step 1
First graph function $$\displaystyle{y}=\sqrt{{{x}}}$$
Then, to obtain graph of function $$\displaystyle{f{{\left({x}\right)}}}={1}-\sqrt{{{x}+{2}}}=-\sqrt{{{x}+{2}}}+{1},$$
- shift 2 units to the left
- reflect over x-axis
- shift 1 unit upward
On graph:
Red - $$\displaystyle{y}=\sqrt{{{x}}}$$
Blue - $$\displaystyle{f{{\left({x}\right)}}}=-\sqrt{{{x}+{2}}}+{1}$$
Step 2