91Ó°ÊÓ

Finding a Mathematical Model In Exercises \(41-50\) , find a mathematical model for the verbal statement. Newton's Law of Cooling: The rate of change \(R\) of the temperature of an object is directly proportional to the difference between the temperature \(T\) of the object and the temperature \(T_{c}\) of the environment in which the object is placed.

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minima or maxima. \(f(x)=3 x^{2}-2 x-5\)

Identify any interepts and test for symmetry. Then sketch the graph of the equation. \(y=x^{2}-2 x\)

Snowstorm.During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?

Finding a Mathematical Model In Exercises \(41-50\) , find a mathematical model for the verbal statement. Boyle's Law: For a constant temperature, the pressure \(P\) of a gas is inversely proportional to the volume \(V\) of the gas.

Writing an Equation from a Description In Exercises \(47-54\) , write an equation for the function described by the given characteristics. The shape of \(f(x)=x^{2},\) but shifted two units to the left, nine units up, and then reflected in the \(x\) -axis

Finding an Equation of a Line ,find an equation of the line that passes through the given point and has the indicated slope \(m .\) Sketch the line. $$(8,2), \quad m=\frac{1}{4}$$

Decomposing a composite Function, find two functions \(f\) and \(g\) such that \((f \circ g)(x)=h(x) .\) (There are many correct answers.) $$h(x)=(1-x)^{3}$$

Identify any interepts and test for symmetry. Then sketch the graph of the equation. \(y=-x^{2}-2 x\)

Finding Values for Which \(f(x)=g(x)\) In Exercises \(45-48,\) find the value(s) of \(x\) for which \(f(x)=g(x)\) . $$f(x)=\sqrt{x}-4, \quad g(x)=2-x$$