91Ó°ÊÓ

Graph the function and determine the interval(s) for which \(f(x) \geq 0\). $$ f(x)=9-x^{2} $$

The cost of sending an overnight package from Los Angeles to Miami is $$\$ 23.40$$ for a package weighing up to but not including 1 pound and $$\$ 3.75$$ for each additional pound or portion of a pound. A model for the total cost \(C\) (in dollars) of sending the package is \(C=23.40+3.75 \llbracket x \rrbracket, x>0,\) where \(x\) is the weight in pounds. (a) Sketch a graph of the model. (b) Determine the cost of sending a package that weighs 9.25 pounds.

Find the value(s) of \(x\) for which \(f(x)=g(x)\). $$ f(x)=x^{4}-2 x^{2}, \quad g(x)=2 x^{2} $$

Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) \(y\) is inversely proportional to \(x .(y=7\) when \(x=4\).)

Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=(x+3)^{2}, \quad x \geq-3 $$

Find the slope-intercept form of the equation of the line passing through the points. Sketch the line. $$ \left(2, \frac{1}{2}\right),\left(\frac{1}{2}, \frac{5}{4}\right) $$

Write the standard form of the equation of the circle with the given characteristics. Center: (0,0)\(;\) Radius: 4

Graph the function and determine the interval(s) for which \(f(x) \geq 0\). $$ f(x)=x^{2}-4 x $$

Find a mathematical model representing the statement. (In each case, determine the constant of proportionality.) \(z\) varies jointly as \(x\) and \(y .(z=64\) when \(x=4\) and \(y=8 .)\)

Determine whether the function has an inverse function. If it does, find the inverse function. $$ q(x)=(x-5)^{2} $$