91Ó°ÊÓ

Find the domain of the function. \(f(x)=\log _{9}(|x+3|-4)\)

Find the domain of the function. \(f(x)=\ln (\sqrt{x-4}-3)\)

Find the domain of the function. \(f(x)=\frac{1}{3-\log _{5}(x)}\)

Find the domain of the function. \(f(x)=\frac{\sqrt{-1-x}}{\log _{\frac{1}{2}}(x)}\)

Find the domain of the function. \(f(x)=\ln \left(-2 x^{3}-x^{2}+13 x-6\right)\)

Sketch the graph of \(y=g(x)\) by starting with the graph of \(y=f(x)\) and using transformations. Track at least three points of your choice and the horizontal asymptote through the transformations. State the domain and range of \(g\). \(f(x)=2^{x}, g(x)=2^{x}-1\)

Sketch the graph of \(y=g(x)\) by starting with the graph of \(y=f(x)\) and using transformations. Track at least three points of your choice and the horizontal asymptote through the transformations. State the domain and range of \(g\). . \(f(x)=\left(\frac{1}{3}\right)^{x}, g(x)=\left(\frac{1}{3}\right)^{x-1}\)

Sketch the graph of \(y=g(x)\) by starting with the graph of \(y=f(x)\) and using transformations. Track at least three points of your choice and the horizontal asymptote through the transformations. State the domain and range of \(g\). \(f(x)=3^{x}, g(x)=3^{-x}+2\)

Sketch the graph of \(y=g(x)\) by starting with the graph of \(y=f(x)\) and using transformations. Track at least three points of your choice and the horizontal asymptote through the transformations. State the domain and range of \(g\). . \(f(x)=10^{x}, g(x)=10^{\frac{x+1}{2}}-20\)

Sketch the graph of \(y=g(x)\) by starting with the graph of \(y=f(x)\) and using transformations. Track at least three points of your choice and the horizontal asymptote through the transformations. State the domain and range of \(g\). \(f(x)=e^{x}, g(x)=8-e^{-x}\)