An unknown compound has the following chemical formula: \[ \operatorname{Cr}(\mathrm{OH})_{\mathrm{x}} \] where \( x \) stands for a whole number. Measurements also show that a certain sample of the unknown compound contains 7.90 mol of oxygen and 2.63 mol of chromium. Write the complete chemical formula for the unknown compound.

The graph of \( f(x)=(x-3)^{2} \) is exactly the same as the graph of \( f \) graph of \( f(x)=(x-3)^{2} \) is shifted \( \begin{array}{ll}\text { a } & \text { down } 3 \text { units. } \\ \text { b } \quad \text { left } 3 \text { units. }\end{array} \)

What transformations change the graph of \( f(x) \) to the graph of \( g(x) \) ? \( f(x)=3 x^{2} \) to \( g(x)=9 x^{2}-4 \)

Write the expression as a sum and/or difference of logarithms. Express powers as factors. \( \log _{7}(2401 x) \) \( \log _{7}(2401 x)=\square \) (Type an exact answer in simplified form.)

\( \leftarrow \) Write the expression as a single logarithm. Express powers as factors. \( \ln \left(\frac{x}{x-1}\right)+\ln \left(\frac{x+1}{x}\right)-\ln \left(x^{2}-1\right) \) \( \ln \left(\frac{x}{x-1}\right)+\ln \left(\frac{x+1}{x}\right)-\ln \left(x^{2}-1\right)=\square \)

What are the domain and range of the function defined by \( y=|x+3|-2 \) notation and interval notation? \( \begin{array}{ll}\text { a } \\ \text { domain: }\{x \mid x \geq-3\} ;[-3, \infty) \\ \text { range: }\{y \mid y \geq 0\} ;[0, \infty) \\ \text { domain: }\{x \mid x \geq-3\} ;[-3, \infty) \\ & \text { range: }\{y \mid y \geq 2\} ;[2, \infty) \\ \text { o domain: }\{x \mid x \text { is a real number }\} ;(-\infty, \infty) \\ & \text { range: }\{y \mid y \text { is a real number }\} ;(-\infty, \infty) \\ \text { d domain: }\{x \mid x \text { is a real numbert }\} ;(-\infty, \infty)\end{array} \) range: \( \{y \mid y \geq-2\} ;[-2, \infty) \)