91Ó°ÊÓ

\(45-54=\) A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. \(f(x)=|x| ;\) shift 4 units to the left and shift downward 2 units

Find the inverse function of \(f\) $$ f(x)=\sqrt{2+5 x} $$

Find the domain of the function. $$ f(x)=\sqrt{x-5} $$

Radii of Stars Astronomers infer the radii of stars using the Stefan Boltzmann Law: $$E(T)=\left(5.67 \times 10^{-8}\right) T^{4}$$ where \(E\) is the energy radiated per unit of surface area measured in watts \((\mathrm{W})\) and \(T\) is the absolute temperature measured in kelvins \((\mathrm{K}) .\) (a) Graph the function \(E\) for temperatures \(T\) between 100 \(\mathrm{K}\) and 300 \(\mathrm{K}\) (b) Use the graph to describe the change in energy \(E\) as the temperature \(T\) increases.

Migrating Fish A fish swims at a speed \(v\) relative to the water, against a current of 5 mifh. Using a mathematical model of energy expenditure, it can be shown that the total energy \(E\) required to swim a distance of 10 \(\mathrm{mi}\) is given by $$E(v)=2.73 v^{3} \frac{10}{v-5}$$ Biologists believe that migrating fish try to minimize the total energy required to swim a fixed distance. Find the value of \(v\) that minimizes energy required. NOTE: This result has been verified; migrating fish swim against a current at a speed 50\(\%\) greater than the speed of the current.

Express the function in the form \(f \circ g\) $$ Q(x)=\frac{1}{x+3} $$

\(45-54=\) A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. \(f(x)=x^{2} ;\) shift 2 units to the left and reflect in the \(x\) -axis

Find the domain of the function. $$ f(x)=\sqrt[4]{x+9} $$

Express the function in the form \(f \circ g\) $$ H(x)=\left|1-x^{3}\right| $$

\(45-54=\) A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. \(f(x)=x^{2} ;\) stretch vertically by a factor of \(2,\) shift downward 2 units, and shift 3 units to the right