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

Question
Transformations of functions
asked 2021-02-12
Sketch a graph of the function. Use transformations of functions whenever possible. \(\displaystyle{f{{\left({x}\right)}}}={1}-\sqrt{{{x}}}+{2}\)

Answers (1)

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
image
0

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