Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 1136371: (f + g)(x) = f(x) + g(x) = (x
3 + 1) + (x
2 − 5) = x
3 + x
2 − 4

Click here to see answer by ikleyn(52790)

Question 1136871: Which is the value of g(−5) if g(x)=3.4x−8?

Click here to see answer by ikleyn(52790)

Question 1136945: Given that
f
(
x
)
=
x
2
+
4
x
and
g
(
x
)
=
x
−
9
, calculate
(a)
(
f
∘
g
)
(
x
)
=

(b)
(
g
∘
f
)
(
x
)
=

(c)
(
f
∘
f
)
(
x
)
=

(d)
(
g
∘
g
)
(
x
)
=
Click here to see answer by ikleyn(52790)

Question 1137344: 2. According to the New York Times, the number of people receiving food stamps increased in the early 90’s, but then decreased later in the 90’s. Observe the table below.
Year 1990 1992 1994 1996 1998
Average Monthly Participants
(millions of people) 20.0 25.2 27.3 25.4 19.8
a. Let x = 0 correspond to 1990. Use the regression capabilities of your calculator to determine the equation (linear or quadratic) that best models the data. Explain why you selected the one you did.
b. Use the regression equation to determine the average number of monthly
c. participants in the food stamp program in 1995:
d. Use the regression equation to find when the average number of monthly participants in the food stamp program is exactly 25 million?
e. What was the greatest number of monthly participants in the food stamp program and when did it occur?

f. Identify and interpret the meaning of the vertical intercept.
g. Identify and interpret the horizontal intercepts. Discuss the reasonableness of these values in the context of the problem.

h. State the practical domain and range in the context of the problem.

Click here to see answer by Boreal(15235)

Question 1137571: The graph of y = 4sin (3x + 2) + 1 has amplitude of:
Click here to see answer by ikleyn(52790)

Question 1137894: describe and correct the error,given the functions f(x)=3x - 5 and g(x)=1/3 - 4/3x
1. g(-3) = 1/3 - 4/3(3)
= 1/3 -4 = -32/3
My answer to this was g(-3) = 1/3 - 4/3(-3) = 1/3+4=13/3
2. f(1)= 1/3 - 4/3(1)
=1/3 - 1/4 = -3/3 -1
My answer was f(1) = 3x1 - 5 = 3 - 5 = -2
I was wonder if my answers are correct,if not could someone please explain to me what I did wrong?
Click here to see answer by Boreal(15235)

Question 1137878: A pump is filling a tank with water at a constant rate while water in the tank is also drained by 3 identical pipes.
Starting from a full tank of water with water being pumped into it, the tank can be completely drained by the 3 identical pipes in 35 minutes.
If an additional identical pipe is installed to drain the tank, a full tank of water can be completely drained in 20 minutes when water is pumped into it.
How many minutes will it take for the pump to fill an empty tank with water to its brim without any pipe to drain water from the tank?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1138240: Which set of ordered pairs describe a function:
(2,3),(2,4)
(0,2),(0,3)
(3,0.3),(-3,0.3)
(-2,2),(2,-2)
Click here to see answer by MathLover1(20850)

Question 1138239: Which set of ordered pairs does not represent a function:
(1,2), (1,3), (1,4)
(2,3), (3,3), (4,3)
Click here to see answer by Boreal(15235)

Question 1138461: Let f(x) = (x^2 + 3x + 1), g(x) = (3x + 1) and h(x) = 3x + (2/x). Find (fogoh)(x)
Click here to see answer by MathLover1(20850)

Question 1138717: 1. Find the domain of f(X)=6/(x-2)(x+5)
2. Find the general term of the sequence -2,5,12,19...
Click here to see answer by josgarithmetic(39618)

Question 1138805: The distance S an object travels under the influence of gravity in time t seconds is
given by S t( ) = + gt at +b 1
2
2 where, (g is the acceleration due to gravity), a, b are
constants. Check if the function S t( )is one-one
Click here to see answer by Alan3354(69443)

Question 1138899: is {(-5, -1), (5, -1), (2, -1)} a function

Click here to see answer by MathLover1(20850)

Question 1139075: please explain:
Determine algebraically whether the function f(x)=5 ∛x is even, odd, or neither even nor odd.
thank you,
Click here to see answer by ikleyn(52790)

Question 1139148: 3. If F = { (1,2), (3, 5), (4,7)} and G = { (1,4), (3,0), and (5, 2)}, what is F + G? What is F/G (using arithmetic function)?
Click here to see answer by ikleyn(52790)

Question 1139295: For the functions f(x) =3x +9 and g (x) = 2x-4, find (f+g) (0)
Need this solved step by step line by line in different ways.
Click here to see answer by josgarithmetic(39618)

Question 1139628: Inverse od F-1(3) & F-1(8)? How do I do it?
Click here to see answer by MathLover1(20850)

Question 1139678: If f(x + y) = f(x) + f(y) and f(1) = 3, Find f(2), f(3), and f(4). Is f(x + y) = f(x) + f(y) for all
functions?

Click here to see answer by ikleyn(52790)

Question 1140172: For the function f(x)=3x-5/√2x-1 find f(-2) and f(z-1)
Click here to see answer by josgarithmetic(39618)

Question 1140249: g(x)= sqrt ( x-4-4 )

Find g(7)
Click here to see answer by josgarithmetic(39618)

Question 1140316: For the function g(x)=(3/2) x-5, find g(4a)-g(a).
Click here to see answer by Boreal(15235)

Question 1140316: For the function g(x)=(3/2) x-5, find g(4a)-g(a).
Click here to see answer by josgarithmetic(39618)

Question 1140315: Given the function defined by g(x)=(5x-7), find g(1/5)

Click here to see answer by Boreal(15235)

Question 1140314: If r(x)= (7/x-7)
, find r(7.5).
Click here to see answer by Boreal(15235)

Question 1140313: For the function g(x)= (1/2) x-4
, find g(2a-4)
Click here to see answer by josgarithmetic(39618)

Question 1140317: If r(x)=(6/x-7)
, find r(a^2)
answer is one fraction.
Click here to see answer by josgarithmetic(39618)

Question 1140322: For the function g(x)=(3/2) x-8, find g(4a)-g(a).
Click here to see answer by Boreal(15235)

Question 1140320: If r(x)=(5/x-2)
, find r(a^2) and write the answer as one fraction.
Click here to see answer by Boreal(15235)

Question 1140321: For the function g(x)=(1/3) x-8
, find g(3)+g(a)
Click here to see answer by MathLover1(20850)

Question 1140318: For the function g(x)=(1/2) x-2
, find g(2)+g(a)
Click here to see answer by MathLover1(20850)

Question 1140359: Consider the circle x^2 + y^2 - 2x -14y +25=0
Show that, if the line y=mx intersects the circle in two distinct points, then (1+7m)^2 -25(1+m^2) > 0
Click here to see answer by ikleyn(52790)

Question 1140400: please explain if true or false:
f(x) = 2x is an exponential function, but f(x) = x2 is not.
thank you.
Click here to see answer by Alan3354(69443)

Question 1140448: please explain: true / false
True or False: f(x) = 2^x is an exponential function, but f(x) = x^2 is not.
Thank you.
Click here to see answer by Theo(13342)

Question 1141151: Y= (1.3).X
Domain: Range:
Click here to see answer by josgarithmetic(39618)

Question 1141492: Lydia holds the end of a yo-yo string 0.9 metres from the ground and swings the yo-yo in a circle perpendicular to the ground. After 0.5 seconds, the yo-yo is at it’s closest point to the ground, 0.1 metres. After 1 second, the yo-yo is at its farthest point from the ground, 1.7 metres. What is the amplitude of the function that represents the yo-yo’s distance from the ground in terms of the seconds that have passed, and what does it represent?

Click here to see answer by ikleyn(52790)

Question 1141493: A certain planet has a day length of 24 hours. The planet is totally covered in water, except for one small island. At hour 0, the island has 100% light with the planet’s star in the top of the sky. At hour 12, the island has 0% light and is in total darkness. Write an equation that models the amount of light in the sky on the island in terms of hours passed.

Click here to see answer by ikleyn(52790)

Question 1141495: without graphing determine the amplitude, period, domain, and range of the function of the function y=-2.3sin (5x)+7
Click here to see answer by ikleyn(52790)

Question 1141495: without graphing determine the amplitude, period, domain, and range of the function of the function y=-2.3sin (5x)+7
Click here to see answer by Theo(13342)

Question 1141496: A spring bounces up and down according to the model d(t)=3sin(30t)+2, where d(t) is the displacement in cm from the rest position and t is time in seconds.
a) What is the amplitude of the function?
b) Is this the same as the maximum displacement from the rest position? Explain.
c) What is the equation of the axis?
d) Explain why the function models periodic behaviour.
Click here to see answer by ikleyn(52790)

Question 1141497: a) Determine the equation of a sine function that would have a range of {y ER|-4≤y≤1}
and a period of 45degrees.
b) Determine the cosine function that results in the same graph as the function in part (a).
Click here to see answer by ikleyn(52790)

Question 1141532: https://snag.gy/kD2AoW.jpg
Click here to see answer by ikleyn(52790)

Question 1141533: a) Determine the equation of a sine function that would have a range of {yER|-4≤y≤1} and a period of 45 degrees.
b) Determine the cosine function that results in the same graph as the function in part (a).
Click here to see answer by Alan3354(69443)

Question 1141531: A fish is caught in a water wheel. A graph of its height (in metres) with respect to the surface of the water over time is shown below.
https://snag.gy/eG3ytX.jpg
a) What is the diameter of the water wheel?
b) How long does it take the fish to complete one revolution of the wheel?
c) Does the fish reenter the water? If so, for approximately how long?
d) After 36 seconds, at what height will the fish be?

Click here to see answer by Alan3354(69443)

Question 1141539: Please help. Thank you
A fish is caught in a water wheel. A graph of its height (in metres) with respect to the surface of the water over time is shown below.
Graph in the link: https://snag.gy/En4HMW.jpg
a) What is the diameter of the water wheel?
b) How long does it take the fish to complete one revolution of the wheel?
c) Does the fish reenter the water? If so, for approximately how long?
d) After 36 seconds, at what height will the fish be?
Click here to see answer by Alan3354(69443)

Question 1141494: A fish is caught in a water wheel. A graph of its height (in metres) with respect to the surface of the water over time is shown below.
https://snag.gy/jFuUZK.jpg
a) What is the diameter of the water wheel?
b) How long does it take the fish to complete one revolution of the wheel?
c) Does the fish reenter the water? If so, for approximately how long?
d) After 36 seconds, at what height will the fish be?
Click here to see answer by josmiceli(19441)

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