74. A point P in the first quadrant lies on the graph of the function f(x) = . Express the slope of the line joining P to the
origin as a function of x.
22)
______
A)
77. A point P in the fourth quadrant lies on the graph of the function f(x) = . Express the slope of the line joining P to the
origin as a function of x.
23)
______
A)
266. Graph the functions f(x) = and g(x) = 3 + together to identify the values of x for which > 3 + .
Confirm your findings algebraically.
73)
______
A)
275. The kinetic energy K of a mass is proportional to the square of its velocity v. If K = 14,450 joules when what
is K when v = 13 m/sec?
76)
______
A)
278. Boyle's Law says that volume V of a gas at constant temperature increases whenever the pressure P decreases, so that V
and P are inversely proportional. If P = 14.1 lbs/ when V = 900 , then what is V when P = 21 lbs/ ?
77)
______
A)
281. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 inches by 29
inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the
volume V of the box as a function of x.
78)
______
A)
285. The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 8 units long.
Express the area A of the rectangle in terms of x.
79)
______
A)
288. A power plant is located on a river that is 600 feet wide. To lay a new cable from the plant to a location in a city 2 miles
downstream on the opposite side costs $ 225 per foot across the river and $ 150 per foot along the land. Suppose that the
cable goes from the plant to a point Q on the opposite side that is x feet from the point P directly opposite the plant. Write
a function C(x) that gives the cost of laying the cable in terms of the
80)
______
A)
429. The accompanying figure shows the graph of y = - shifted to a new position. Write the equation for the new graph.
124)
_____
A)
430. y = -(x - 3)
2
- 2
B)
y = -(x + 3)
2
+ 2
C)
y = -(x - 2)
2
- 3
D)
y = -(x + 3)
2
- 2
Answer
431. D
The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an
equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid
line.
125)
525. D [-6, 3]; R [-2, 4]
B)
D [-7, 2]; R [-2, 4]
C)
526. D [-3, 6]; R [-2, 4]
D)
D [-7, 2]; R [-2, 4]
Answer
527. A
The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give
an equation for the stretched or compressed graph.
149)
528. y = + 4 stretched horizontally by a factor of 3
149)
_____
A)
529. y = 3 + 12
B)
y = + 4
C)
y = 9 + 4
D)
y = + 4
Answer
565. C
Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State
whether the combination of functions (where defined) is even or odd.
160)