What transformations of the parent graph of f(x)=sqrt{x} produce the graphs of the following functions? a) m(x)=sqrt{7x - 3.5} - 10 b) j(x)=-2sqrt{12x} + 4

Question
Transformations of functions
asked 2021-01-06
What transformations of the parent graph of
\(\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{x}}}\)
produce the graphs of the following functions?
a) \(\displaystyle{m}{\left({x}\right)}=\sqrt{{{7}{x}\ -\ {3.5}}}\ -\ {10}\)
b) \(\displaystyle{j}{\left({x}\right)}=-{2}\sqrt{{{12}{x}}}\ +\ {4}\)

Answers (1)

2021-01-07
Step 1
First we are going to graph the prent function and the first transformation and second transformation of parent function.
image
Step 2
As we can see from the graph the first transformation of parent function has horizontal shift of 0.5 units to the right, and vertical shift of 10 units down. Vertical stretch was also preformed on the first function.
The second transformation of parent function has been reflected across x-axis and vertically shifted up 4 units. Horizontal compression was also preformed on the for the second function.
0

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