Math 107 Quiz 3
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The quiz is worth 100 points. Each problem is worth 5 points.
1.
For the given graph, please determine the intervals where the graph is
(a) increasing, (b) decreasing, or (c) constant.
2.
Determine the intervals where the graph is increasing, and also any relative maxima or minima.
3. (a) The area of a rectangle formula is A = lw. Suppose that
the width is 5 less than the length. Express area as a
function of the width.
(b) Use the function that you got from (a) to find the area
when the width is 10 inches. Please make sure to give
an appropriate unit of area.
4. A hot-air balloon rises straight up from the ground at a rate of 120 ft/min.
The balloon is tracked from a rangefinder on the ground at point P, which is
400 ft from the release point Q of the balloon. Let d = the distance from the
balloon to the rangefinder and t = the time, in minutes, since the balloon was
released. Express d as a function of t. (HINT: Please use the Pythagorean
Theorem which says a2 + b2 = c2).
5. Graph the piecewise function given by
Then, determine the domain and range.
6. Given the function f( x ) = x3 – x + 20 and g( x ) = 10x2, find
each of the following (NOTE: each part is independent from
the other).
(a) (f + g)(x)
(b) (g – f)(x)
(c) (ff)(x)
(d) (gf)(x)
(e) (f/g)(x)
7. Given the function f( x ) = x3 – x + 20 and g( x ) = 10x2, find
each of the following (NOTE: each part is independent from
the other).
8. Given the revenue function, R(x) = 60x - .4x2 and the cost function,
C(x) = 3x + 13, and using the fact that P(x) = R(x) – C(x), please find
(a) P(x)
(b) P(10)
10. The graph of y = f( x ) is the first graph shown and y = g( x ) is the graph
shown just underneath that. (No formulas are given.) Please choose which
best describes the relationship between the two graphs. HINT: Please find
points on each of y = f( x ) and y = g( x ) and compare the points on y = f( x )
and y = g( x ).
(a) g( x ) = f( x + 1) – 2
(b) g( x ) = f( x – 1 ) + 2
(c) g( x ) = f( x + 2 ) + 1
(d) g( x ) = f( x – 2 ) + 1
11. In the following sentence, please fill in each blank with
either of the words “up”, “down”, “right”, or “left”.
The graph of y = | x + 7 | - 2 is the graph of y = | x | moved
_______ 7 units and ______ 2 units.
12. Given that (3, 4) and (1, -2) are points on the graph of y = f( x ), please
list each of the corresponding points on the graph of y = -f( x ).
13. Given that (3, 4) and (1, -2) are points on the graph of y = f( x ), please
list each of the corresponding points on the graph of y = 4f( x ).
14. Please feel free to use the graph of the equation or test algebraically to
determine the kinds of symmetry that each of the following equations have.
(a) y = | 5x |
(b) xy = 12
(c) y = 1
(d) x2 + y2 = 9
15. Please feel free to use the graph of the equation or test algebraically to
determine whether the following equation is an odd function, an even
function, a function that is neither odd nor even, or a function that is both
odd and even.
(a) y = | 5x |
(b) xy = 12
(c) y = 1
16. Find a point that is symmetric to (1, 2) with respect to the x-axis,
y-axis, and the origin.
FOR #17 AND #18, FIND THE VARIATION CONSTANT AND AN
EQUATION OF VARIATION FOR THE GIVEN SITUATION.
17. y varies directly as x, and y = .1 when x = .2.
18. y varies inversely as x, and y = .2 when x = 35.
19. The weight M of an object on the moon varies directly as its weight
E on earth. A person weighs 169.76 lbs on earth weighs 28.86 lbs
on the moon. How much would a 241.76-lb person weigh on the
moon?
20. The stopping distance d of a car after the brakes have been applied
varies directly as the square of the speed r. If a car traveling
60 mph can stop in 200 ft, how fast can a car travel and will stop in
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