91Ó°ÊÓ

Determine the appropriate functions. A city does not tax the first 30,000 dollars of a resident's income but taxes any amount over 30,000 dollars at \(5 \%\). (a) Find the tax \(T\) as a function of a resident's income \(I\) and (b) find \(f(25,000)\) and \(f(45,000)\).

Solve the given problems. A demolition ball is used to tear down a building. Its distance \(s\) (in \(\mathrm{m}\) ) above the ground as a function of time \(t\) (in s) after it is dropped is \(s=17.5-4.9 t^{2} .\) Because \(s=f(t),\) find \(f(1.2)\)

A function and how it is to be shifted is given. Find the shifted function and then display the given function and the shifted function on the same screen of a graphing calculator. \(y=-4 x,\) up \(4,\) right 3

A function and how it is to be shifted is given. Find the shifted function and then display the given function and the shifted function on the same screen of a graphing calculator. y=\sqrt{2 x+1}, \text { up } 1, \text { left } 1

Solve the given problems. A spherical buoy 36 in. in diameter is floating in a lake and is more than half above the water. (a) Express the circumference \(c\) of the circle of intersection of the buoy and water as a function of the depth \(d\) to which the buoy sinks. (b) Find the domain and range of the function.

In Exercises \(37-66,\) graph the indicated functions. On a taxable income of \(x\) dollars, a certain city's income \(\operatorname{tax} T\) is defined as \(T=0.02 x\) if \(0 < x \leq 20,000\) \(T=400+0.03(x-20,000)\) if \(x > 20,000 .\) Graph \(T=f(x)\) for \(0 \leq x < 100,000\)

Graph the indicated functions. The temperature \(T\) (in \(^{\circ} \mathrm{C}\) ) recorded on a day during which a cold front passed through a city was \(T=2+h\) for \(6