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Water is flowing into each of the bottles as shown at a steady rate.  Match each bottle shape with the graph of the heightof  the water as a function of time.The graphs are as follows: These are the bottles:Answer: → Graph A, → Graph C, → Graph BFind the length and midpoint of th...

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Water is flowing into each of the bottles as shown at a steady rate. Match each bottle s ofthe water as a function of time. The graphs are as follows:

These are the bottles:

Answer:

→ Graph A,

→ Graph C,

→ Graph B

Find the length and midpoint of the interval from x=9 to x=-2. (use decimal values for fr



Answer: length =



and midpoint x =

Answer: 3.5 Answer: 11

Find the slope of the line which is tangent to the circle with center C(3,1) at the point P(8



Answer: slope of the tangent line Answer: 12

Find an equation describing all pointsP(x,y) equidistant from Q(-3,4) and R(1,-3). (use th input the numerical coefficient of each term of the equation below)



Answer: x -

 Answer: 8

 Answer: 14

Answer: 0 Answer: 15

Find the line which goes through the point (2,-5) and is perpendicular to the line 3y-7x= of each term to complete the required equation) Answer:



Answer: x +

 Answer: 3

Answer: 7

Answer: 29

Given f(x) = x2 + 1 and g(x) = x/(x-10). Evaluate: a. f(2) and g(2); b. f(5x) and g(5x); c that fractional answers must be expressed like -5/6, and answers with exponents lik case letters.and do not use spaces in your answers. Answer: a. f(2) =



and g(2) = Answer: 5

Answer: -1/4

b. f(5x) = Answer: 25x^2+1

Answer: x/(x-2)

and g(x) = Answer: x^2-4n+4n^2+1

Answer: (x-2n)/(x



c. f(x-2n) =



and g(x-2n) =

Find the slope of the line through the points P and Q when: a. P(1,3) and Q(x, x 2+3x-1) b. P(x, x2+3x-1) and Q(x+h, (x+h) 2+3(x+h)-1) 

Answer: a. m =



b. m = Answer: x+4 Answer: 2x+h+3

Let f(x)=x+1 and define s(x) to be the slope of the line through the points (0,0) and s(-2); b. Find an equation for s(x) in terms of x. Note that fractional answers must be expressed like 5/6 and answers with expone

Define A(x) to be the area of the rectangle bounded by the axes and the line y=2, a in the figure.

 a. Evaluate A(2) and A(5) b. Find an equation for A(x) in terms of x. Answer: a. A(2) =



and A(5) =

Answer: 4

Answer: 10

b. A(x) =

Answer: 2x

A function f is given by f(4x-1) = 4x2+5. Evaluate f(15). 

Answer: f(15) =

Answer: 69

For f(x) = 3x-2 and g(x) = x 2+1, find the composite function defined by f o g(x) and Note: For exponential answer, express it like x^3 for x cubed. Use lowercase letter answer. Answer: f o g(x) = g o f(x) =

 Answer: 3x^2+1 Answer: 9x^2-12x+5

Given:

Evaluate f(3), g(-1), and h(4).

What is the slope of the line through (3,9) and (x,y) for y=x 2 and x=2.97? x=3.001? x=3 slope when h is very small (close to 0)? Round-off your answers to 2 decimal places, wh Answers: (Write the letter first before the number, say h+1) Slope at x=2.97 =



Slope at x=3.001 = Answer: 5.97 Slope at x=3+h = Answer: 6 Slope when h is close to 0 Answer: h+6 Answer: 6 The figure shows the distance of a car from a measuring position located on the edge o (a) What was the average velocity of the car from t=10 to t=30 seconds? (b) What was the average velocity of the car from t=20 to t=25 seconds?

Answers: (a) average velocity =



feet/second (b) average velocity = feet/second

Answer: 10 Answer: -20

From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the h line at x. For example A(4)=12 is the area of the 4 by 3 rectangle. (a) Evaluate A(2.5) (b) Evaluate A(4) - A(1)

The figure shows the temperature during a day in a place. How fast is the temperature P.M.? Round-off your answer to 2 decimal places.



Answer: 0F/hour

Answer: -1.67

Evaluate



Answer:

Answer: 2

Evaluate



Answer: /



Answer: 108

Answer: 7

Evaluate



Answer: /



Answer: 1

Answer: 6

Evaluate

Answer: Answer: 4

Answer: 3

Answers: (a)



(b) Answer: 1 (c) Answer: 2 Answer: 3 Use the functions f and g defined by the graphs as shown to determine the following lim (a) (b)

Answers: (a) (b)

 Answer: 2 Answer: 4/3

Use the function h defined by the graph as shown to determine the following limits: (a) (b)

Answers: (a) (b)



Answer: 1 Answer: 1

Use the function h defined by the graph shown to determine the following limits: (a) (b)

Answers: (a) (b)



Answer: 1 Answer: -2

Use the graph below to determine the right-hand limit of the function f(x) at: (a) x=-8 (b) x=6

Answers: (a)



(b) Answer: -6 Answer: 5 At which values of x is the function from the graph shown continuous? State the answer there would be more than one.

Answers: x=



x= Answer: -1 Answer: 2 At which values of x is the function from the graph shown discontinuous? State the answ if there would be more than one.

Given a function f, an interval [a,b] and a value V. Find a value c in the interval so that f( Value Theorem. NOTE: Round-off your answers to 2 decimal places, stating from the least to the highest one. For positive answers, do not state the + sign anymore. For answers less than 1, pre (a)

on [0,3], V = 2

(b) Answers: (a) c = Answer: -1.41

Answer: 1.41

; c = Answer: 0.52



(b) c =

Use the Bisection Algorithm Method to find the root of the given function to an interval 0.1. Answer should be up to one decimal place only. f(x) = x2 - 2 on [0,3]



Answer:

Answer: 1.4 Given the followi Mark 0.00 out of 3.00

Answers: f(1) =



g(9) =

Answer: 4

h(4) =

Answer: 2 Answer: 2

Find the point of intersection and the angle between x - y = 32 and 3x - 8y = 6. Answers: Point of Intersection = ( ,



 ) Answer: 50

Answer: 18

Angle of Intersection = Answer: -24.44

Find the point of intersection and the angle between 2x - 3y = 3 and 4x - 2y = 10. Answers:



Point of Intersection = (

 )

,

Answer: 3

Answer: 1

Angle of Intersection = Answer: 29.74 0

 (round-off to 2 decimal places)

What is the slope of the line through (-1,-2) and (x,y) for y = x 2 + x – 2 and x=-0.98. Rou places whenever possible.



Answer: slope =

Answer: -0.98 Find the equation of the line passing through the point (-1,2) and parallel to the line y=2 intercept form. Do not use any space between the letter (lower case), symbol and num



Answer: 

Answer: y=2x+4

Find the equation of the line through the point (3,4) and parallel to the x axis. Do not us (lower case), symbol and number, say x+y=1 Answer:



 Answer: y=4

Find the equation of the line through the point (-1/2,-2) and parallel to the line 4x + y = form. Do not use any space between the letter (lower case), symbol and number, say x Answer:



 Answer: 4x+y+4=0

Find the equation of the line passing through the point (6,3) and perpendicular to the lin in general form. Do not use any space between the letter (lower case), symbol and num Answer:



Find the equation of the tangent line to the circle with center at (-3,1) at point (-2,5). Wr Do not use any space between the letter (lower case), symbol and number, say x+y-1=0



Answer: 

Answer: x+4y-18=0

Find the equation of the tangent line to the circle with center at (1,-3) at point (5,-2). Wr Do not use any space between the letter (lower case), symbol and number, say x+y-1=0



Answer: 

Answer: 4x+y-18=0

Find the equation of the tangent line to the circle with center at the origin, at point (9,7) form. Do not use any space between the letter (lower case), symbol and number, say x



Answer: 

Answer: 9x+7y-130=0

Find the coordinates of the midpoint R between Q(5,3) and S(7,-5). Answer: R = ( ,



 ) Answer: 6

Answer: -1

Find the length and the midpoint of the interval from x=12 to x=-6.



Answers: length = , midpoint x =

Answer: 18

Answer: 3

Find an equation describing all points P(x,y) equidistant from (-2,4) and (5,-1). Write you not use any space between the letter (lower case), symbol and number, say x+y-1=0 Answer:



Answer: 7x-5y-3=0 Find the slope and midpoint of the line segment from (1,2) to (n+1,3n+2). Use decimal 2 7 Do not use any space between the letter (lower case) symbol and number.

You are at the origin (0,0) and are watching a small bug at thepoint (t, 1+t 2) at time t your line of vision when t=5 seconds and when t=7 seconds? Use fractional answer, wh 11/22 Answers:



@ 5 sec =

Answer: 26/5

@ 7 sec =

Answer: 50/7 Find the equations of 2 lines that both go through the point (3,-2), one with slope 4 and answer in general form. Do not use any space between the letter (lower case), symbol Answers:



when slope is 4 = when slope is -1/4 =

Answer: 4x-y-14=0  Answer: x+4y+5=0

Find a value for B so that the line y = 10x – B, goes through the point (5,-5). Answer: B =



Answer: 55 A kite at an altitude of 30 feet is flown by a boy in the West direction at 2 feet per secon string 30 seconds after it passes the boy overhead?



Answer: slope = /

 Answer: 1

Answer: 2



Find a value for A so that the line 4x-y+A=0 goes through the point (-6,5). Answer: A =



Answer: 29 What are the coordinates of a circle with standard equation x2 +y2 = 49? What is the va Answer: Center (0,



Find the point of intersection and the angle between 2x-y+3=0 and 3x+y-1=0. Use dec



Answer: point of intersection is (-0. ,

 ) Answer: 4

Answer: 2.2

angle of intersection is Answer: 11.31 degrees (round-off to 2 decimal places)

How far from the bottom of a wall will a 30 feet long ladder reach the ground if the top feet vertically from the ground? What will be the slope of the ladder ? What angle will th



Answer: feet along the gr slope of the ladde

f to 2 decimal places) Answer: 28.91

 Answer: 2767

(4 decimal places)

angle of the ladder with the ground =

Answer: 15.47

degrees (round-off to 2 decimal places)

Find the equation of the line tangent to the circle x2 + y2 = 36 at point (11,5). Use the g your final answer.



Answer: x+

 Answer: 11

Answer: 5

Answer: 146

Find the coordinates of the midpoint P between S(-5,7) and T(3,9).



Answer: P( ,

 ) Answer: -1

Answer: 8

Find the equation of the lines that are both passing through the point (-5,6) with slopes Answer:



x - 3y + Answer: 2

Answer: 28

Find the equation of the line which contains the point (7,-1) and is parallel to the line 6x-



Answer: x - y -

Answer: 3

Answer: 22

From the figure shown, find the values of f(2), f(-1) and f(0).

Answers: f(2) =



f(-1) = Answer: 5 f(0) = Answer: 2  Answer: 1

From the graph shown, find the values of f(-3), f(-1), f(0), and f(1).

Answers: f(-3) = f( 1)



Let f(x) = 2-x2, evaluate (a) f(x+1) and (b) f(x)+f(1). Answers: (a) f(x=1) = -x2 -



(b) f(x) + f(1) = -x2 + Answer: 2x+1 Answer: 3 Let f(x) = 1-(x-1)2 evaluate Answers:



(a) (b)

Answer: 0 Answer: 8/9

Find the slope of the line through (-5,3) and (x+1, x-2).



Answer: m =

Answer: x-5/x+6 Evaluate Answer: /

  Answer: 1

Evaluate Answer:

 Answer: 5

Evaluate  Answer:

 Answer: 2

Evaluate

Answer: 10

Evaluate Note:



Answer:

Answer: 2 Mark 0.00 out of 3.00 Write the contrapositive of the statement: If I exercise and eat right, then I will be health answer.



Answer: If I

Answer: am not cise and eat right Answer: do not

healthy, then I

Write the negation for the statement: All quadratic equations have solutions.



Answer:

 solutions.

all quadratic equ Answer: Not

Answer: have

What is the slope of the tangent line through (3,2) and (x,y) for x=-2 and y=x 3. Answer: m =



Answer: 2 The equation of motion is given by s(t) = 6t2 + t + 8 at 1:05 P.M. What is the average ve in meters/second? Answers: @ 1:07 P.M., t =



minutes; s(t) =

Answer: 2ers

Answer: 34

@ 1:09 P.M., t =

Answer: 4

Answer: 96

minutes; s(t) = Average velocity = m/sec

Answer: 31 

How far up a wall will a 25 foot long ladder reach if the bottom must be at least 6 feet fr will be the slope of the ladder if the bottom is 6 feet from the wall? What angle will the l



Answer: feet up the wall ( slope of the ladde

decimal places) Answer: 24.27



Answer: 4.045

(3 decimal places)

angle of the ladder with the ground =

Answer: 76.11

degrees (round-off to 2 decimal places)

Find the equation of the line tangent to the circle x2 + y2 = 25 at point (3,4). Use the ge final answer.



Answer: 3x +

 = Answer: 4

y-

Answer: 25

Find the coordinates of the midpoint R between P(4,-5) and Q(6,5). 



Answer: R( ,

 ) Answer: 5

Answer: 0

Find the equation of the lines that are both passing through the point (10,-8) with slopes



Answer: x - y -

Answer: 5

Answer: 58

x + Answer: 5 y +

Answer: 30

 =0

ForP=(5,2) and Q=(7,-11),Δx,Δy, and the slope of the line segment from P to Q. (use de Answer:Δx =



A small airplane at an altitude of 5000 feet is flying East at 300 feet per second, and you telescope as it passes directly overhead. Refer to the figure above. a. What is the slope of the telescope 5, 10, and 20 seconds after the plane passes overhe b. What is the slope of the telescope t seconds after the plane passes overhead? c. After it passes overhead, is the slope of the telescope increasing, decreasing, or stayin The solution for the first requirement from question a is provided as follows:



Answer: a. at 10 sec, slope =   at 20 sec,slope = 0.

 Answer: 1.67

Answer: 83

b. slope at t seconds = Answer: 16.67 /t c.

Answer: decreasing

Find the equations for two lines that both go through the point (1,2), one with slope 3 an numerical coefficient of each term to complete the required equation)

From the graph shown, find: a. f(-1) b. f(0) c. 3f(2) d. the value of x that corresponds to f(x)=0

Answers:



a. f(-1) = b. f(0) =

Answer: 2 c. 3f(2) = Answer: 1



d. x =

Answer: -21 Answer: 1 Let f(x)=1-(x-3)2 , evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1). Answers: (a)



Answer: 1

Answer: x

Answer: 1

Answer: x

(b) Answer: -4 (c) x2 +

Answer: 8x-3

 

Given the function f(x)=3x-4, evaluate: (a) f(x-2), (b) f(x)-f(2), (c) f(1)/f(3), and (d) f(1/3). U Answers:

Given g(t) =

, evaluate: (a) g(5) and (b) g(2s - 5)

Answer:



(a) g(5) = (b) g(2s-5) =

Answer: 5/2

 Answer: s/s-3

Find the slope of the line through (-3-1) and (x+3, y+1).



Answer:

Answer: y/x Evaluate



Answer:

Answer: 1

Evaluate



Answer: /



Answer: 108

Answer: 7

Evaluate



Answer: /



Answer: 1

Evaluate Answer:

 Answer: 10

Answer: 4

Write the contrapositive of the statement: If x2 + x - 6 = 0 then x=2 or x=-3.



Answer: If x = and x =



- 6 is not e Answer: 2

Answer: 3

What is the slope of the tangent line through (0,-3) and (x,y) for y = 3x 2 - 3 and x=1?



Answer: m =

Answer: 3 An object is dropped from the top of ABC Tower, 1,500 feet from the ground. Calculate over the interval t=2 seconds and t=3 seconds. The position function of the projectile is is the initial velocity of the object and h 0 is the height to which it is dropped. Answers:



at t=2 seconds, s(t) = feet

Answer: 1436

at t=3 seconds, s(t) =

Answer: 1354

feet average velocity =

Answer: 82

ft/sec

Find the slope of the line passing through the points (3,-4) and (-6,9). Use decimal value



Answer:

Answer: -1.44

Find the equation of the line passing through (-2,3) and perpendicular to the line 4x=9-2 the line for your final answer.



Answer: x y+

 = Answer: 2

Answer: 8

Find the equation of the line which goes through the point (3,10) and is parallel to the lin



Answer: x - y -

Answer: 7

Answer: 11

Given g(x)= (x+3)/(x-1). Evaluate g(5) and g(2n+1). Note that fractional answers must be expressed like -5/6, and answers with expone lower case letters.and do not use spaces in your answers. Answer: 

g(5) =



and g(2n+1) = Answer: 2

Answer: (n+2)/n



Find the s...