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

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Begin by graphing \(\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}\) Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. \(\displaystyle{r}{\left({x}\right)}={{\log}_{{{2}}}{\left(-{x}\right)}}\)

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asked 2021-01-28

Begin by graphing \(\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}\) Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each functions domain and range. \(\displaystyle{g{{\left({x}\right)}}}=\ -{2}{{\log}_{{{2}}}{x}}\)

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asked 2021-01-10

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Answer 1

Step 1
First we are going to graph the prent function and the first transformation and second transformation of parent function.

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.

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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

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