Determine the intervals on which the following function is increasing or decreasing, and any relative maxima or minima.

Determine the intervals on which the following function is increasing or decreasing, and any relative maxima or minima.

1). –|x + 5| – 3

 

Find the domain and range of the following piecewise function.

2). ? –x + 2, for x ? 0
f(x) = {
? x – 3, for x > 0
Given that f(x) = 1/x and g(x) = , find the following, and determine the domain of each.

3). ( f / g )(x)
4). ( g – f )(x)
Find ( f ? g )(x) and ( g ? f )(x) (these are composite functions), and the domain of each.

1 x + 2
5). f(x) = ———- , g(x) = ———-
x – 2 x

 

Determine whether the following functions are even, odd, or neither even nor odd.

6). f(x) = |x – 2| + 3
x2 + 1
7). ————–
x3 – 1

Write an equation for the following functions that has a graph with the following given characteristics.

8). The shape of y = x3, but shifted right 5 units and shifted down 11 units.

9). The shape of y = x2, but stretched horizontally by a factor of two, and shifted down 3 units.

10). The volume V of a given mass of a gas varies directly as the temperature T, and inversely as the pressure P. If the volume V = 231 cm3 when the temperature T = 42? and pressure P = 20 gm/cm2, then what is the volume when T = 30? and P = 15 gm/cm2.

11). Wind resistance, or atmospheric drag, tends to slow down moving objects. Atmospheric drag varies jointly as an object’s surface area and velocity v. If a car traveling at a speed of 40 mph with a surface area of 37.8 ft2 experiences a drag of 222N (Newtons), then how fast must a car with 51 ft2 of surface area travel in order to experience a drag force of 430 N?

 
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