# Math 107 quiz 3 | Mathematics homework help

**IN ORDER TO GET FULL CREDIT FOR EACH PROBLEM, PLEASE SHOW ALL WORK AND WRITE EVERYTHING OUT CORRECTLY USING THE LANGUAGE OF MATH. **

**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. Expressarea 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 a^{2} + b^{2} = c^{2}).

5. Graph the piecewise function given by

Then, determine the domain and range.

6. Given the function f( x ) = x^{3} – x + 20 and g( x ) = 10x^{2}, 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 ) = x^{3} – x + 20 and g( x ) = 10x^{2}, find

each of the following (**NOTE**: each part is independent from

the other).

(a)

(b)

(c)

8. Given the revenue function, R(x) = 60x – .4x^{2} 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)

9. Given that f( x ) = x^{2}, please find the difference quotient, .

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) x^{2} + y^{2} = 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

(d)

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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