91Ó°ÊÓ

The graph of \(f(x)=10^{x}\) is refl cted about the \(x\) -axis and shifted upward 7 units. What is the equation of the new function, \(g(x) ?\) State its \(y\) -intercept, domain, and range.

The graph of \(f(x)=10^{x}\) is reffected about the \(x\) -axis and shifted upward 7 units. What is the equation of the new function,g(x)? State its \(y\) -intercept, domain, and range.

For the following exercises, identify whether the statement represents an exponential function. Explain. The value of a coin collection has increased by \(3.25 \%\) annually over the last 20 years.

For the following exercises, use like bases to solve the exponential equation. $$ 3^{2 x+1} \cdot 3^{x}=243 $$

For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. $$ \log _{4}\left(\frac{\frac{x}{z}}{w}\right) $$

The graph of \(f(x)=(1.68)^{x}\) is shifted right 3 units, stretched vertically by a factor of \(2,\) refl cted about the \(x\) -axis, and then shifted downward 3 units. What is the equation of the new function, \(g(x) ?\) State its \(y\) -intercept (to the nearest thousandth), domain, and range.

For the following exercises, state the domain and range of the function. $$f(x)=\log _{3}(x+4)$$

The temperature of an object in degrees Fahrenheit after \(t\) minutes is represented by the equation \(T(t)=68 e^{-0.0174 t}+72 .\) To the nearest degree, what is the temperature of the object after one and a half hours?

For the following exercises, rewrite each equation in exponential form. $$\log _{4}(q)=m$$

For the following exercises, use like bases to solve the exponential equation. $$ 2^{-3 n} \cdot \frac{1}{4}=2^{n+2} $$