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

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1)E(t)=1225(t)+2700------->I arrived at the 1225 by 12500-2700/8(years)=1225
:
2)f(g(-3))===
:

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domain is values of x so just plug them into the equation and solve for y
:
range is {2,3,4,6}

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find the lcd...it is 8
:
or 1 3/8

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You need to reword your question to be more clear. I do not understand what the question is. I think you may be asking how to reduce a matrix to solve a system of linear equations, but I honestly cannot tell from your post.

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8X/24=x/3 ans.

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=

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Let = cost per book
Let = number of books bought per customer
given:

= money spent on books per customer
= maximum books allowed
----------------

given:

I'm not real sure what is wanted. I think it's

Divide through by

She can buy between 1 and 4 books

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The equation for the given line is 9x-3y=5. Rewriting this in standard form we have -3y=-9x+5 or
y =3x-5/3 so the slope is 3

For the line to be determined, using the point slope formula, we have
y-(-1))=3*(x-2)
This can be simplified to y-(-1)+(-1)) = 3x-6+(-1)
So the equation is y=3x-7
I hope that this helps

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Start with the given equation.


Replace EVERY "x" with


FOIL


Distribute

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If A Ç B = {3,1,0}, what are the possible solutions for A and B?

A Ç B = {3,1,0}, then

A and B can be any set such that their only common
elements (members) are 3, 1, and 0.

For example, A could be, say, (3,1,0,2,4) and B could 
be, say, {3,1,0,5,6,7)

Or

For another example, A could be, say, 
A = (3, 1, 0, p, q, z, t) 
and B could be, say, 
B = {3, 1, 0, Connecticut, Florida, Nebraska)

There are infinitely many possibilities unless 
you were given a universal set.

Edwin

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S(n) = the number of tiles required.
The room is square (and assuming the tiles are square):
n = length of room in tile lengths = width of room in tile lengths
So Area of floor = n x n = n^2
So S(n) = n^2
The miniumum length of the room must be 1 tile length for it to be tileable, so domain: n>=1. Sorry for the edit.
This is my first answer I hope it's right and I hope it makes sense.
All the best.

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I have already answered question 3 but here it is again:
Look at a point more closely.
Here is the general point: (x,y)
x = domain
y = range
If any of the x points repeat, then there is no function.
Here is your function:
{(-2,-1),(-1,-4),(0,-5),(1,-4),(3,4)}
Look at the x points and they are:
-2, -1, 0, 1 and 3
Do any of the integers repeat?
No, right?
So, this is a funtion.
The answer is (b).
NOTE: Notice that the range has two -4. You only need to list one of them for the range when numbers repeat. It does not matter if the y values repeat.
The x values cannot repeat because it would take x to two different destinations.
Understand?

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Please list your questions one at a time instead of all questions in one post.
I will the following question below.
3. Find the average rate of change for the function between the given value:
f(x)= sqrt over 2x-1; from 1 to 5
A. 1/2 B. -28 C. -1/6 D. -2 I choosen B. is that correct?
=========================================================
Hello. I will go over the question again SLOWLY. Perhaps I made a mistake. If so, I'll let you know along the way. You said we need to "square over." I assume (2x - 1) lies in the radicand, right?


I will assume that you are talking about the square root of the quantity (2x - 1), which is written as sqrt{2x - 1}.


The average rate of change formula = [f(b) - f(a)]/(b - a)


You were given a function over the interval [1, 5], which means from 1 to 5.


In this case, a = 1 and b = 5.


We now search for f(b), then we search for f(a).
Once we have those two guys, we plug them into the formula above and simplify.


Are you with me so far?


Remember, b = 5 and a = 1 from the given interval.
We plug each number into the function and simplify. By doing so, we will find f(b) and f(a).


Here it is:


f(x) = sqrt{2x - 1}


f(5) = sqrt{2(5) - 1}


f(5) = sqrt{10 - 1}


f(5) = sqrt{9}


f(5) = 3


This means that f(5) = 3 = f(b)


I see what happened. I made a mistake.


The square root of 9 is 3 not 9.


So, f(b) = 3 NOT 9.


Sorry about that....


==========================


We now find f(a).


f(1) = sqrt{2(1) - 1}


f(1) = sqrt{2 - 1}


f(1) = sqrt{1}


f(1) = 1 = f(a).




==========================


We can now plug that info into the formula and simplify.


average rate of change = (3 - 1)/(5 - 1)


average rate of change = 2/4 = 1/2


Dawn, I apologize. The correct answer is 1/2.

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I need help on this one and It is not listedhere and I looked...Help
Determine whether the relation represents a function. If it is a function, state the domain and range.
Problem: {(-2,-1),(-1,-4),(0,-5),(1,-4),(3,4)}
the answers llisted on my sheet is
A. Function, domaion is:{-1,-4,-5,4} and Range is {-2,-1,0,1,3}
B. Function, Domain is ;{-2,-1,0,1,3} Range {-1,-4,-5,4}
C. Not a Function
=======================================================
Look at a point more closely.
Here is the general point: (x,y)
x = domain
y = range
If any of the x points repeat, then there is no function.
Here is your function:
{(-2,-1),(-1,-4),(0,-5),(1,-4),(3,4)}
Look at the x points and they are:
-2, -1, 0, 1 and 3
Do any of the integers repeat?
No, right?
So, this is a funtion.
The answer is (b).
NOTE: Notice that the range has two -4. You only need to list one of them for the range when numbers repeat. It does not matter if the y values repeat.
The x values cannot repeat because it would take x to two different destinations.
Understand?

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Find the domain of x:

It is probably helpful to look at the graph of the function to get an idea of for what values of the independent variable, x, the function, f(x), is defined.

You can see that the function f(x) is defined for all values of x, i.e. x = all real numbers. This means that for every real value of x, the function f(x) has a real (defined) value.

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5) Crossing a wooden bridge at Letchworth Park, Melissa drops a penny into the water below for good luck. If the height of the penny is modeled by the function h(t)=64 - 16t^2, where t represents time in seconds and h(t) is height in feet, how many seconds did it take the penny to hit the water?
(a) 1 (b) 2 (c) 3 (d) 4

===================================================================
Let h(t) = 0
0 = 64 - 16t^2
All you have to do is solve for t.
Can you take it from here?
==================================
Hello. I received your e-mail. You need more help, right?

Here is one of your questions:

(5) Crossing a wooden bridge at Letchworth Park, Melissa drops a penny into the water below for good luck. If the height of the penny is modeled by the function h(t)=64 - 16t^2, where t represents time in seconds and h(t) is height in feet, how many seconds did it take the penny to hit the water?
(a) 1 (b) 2 (c) 3 (d) 4
Let h(t) = 0
0 = 64 - 16t^2
Subtract 64 from both sides.

-64 = -16t^2

Now divide both sides by -16.

-64/-16 = t^2

64/16 = t^2

4 = t^2

Finally take the square root of both sides of the equation.

sqrt{4} = sqrt{t^2}

2 = t

The answer is choice (b).

Do you need help with the trig equation question?

Happy new year!

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F(x-1)=plugging in x-1 for all x's
:
multiplying out
:
combining terms

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The average is the slope of the secant line joining the two points.
-----------------------------------
For the Function,f(x)=x^3+x, find the Average Rate
of change of f from 1 to x:
f(x)-f(1) / (x-1) , x not equal 1
--------------
[(x^3+x) - (1^3+1)]/[x-1]
= [x^3 + x -2] / [x-1]
= x^2 +x + 2
======================
Cheers,
Stan H.

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A function is a set of ordered pairs with the following
restriction: Each x value must have only one y value
associated with it.
====================================
Which of the following are functions? Explain why/why not.
A. f(x)=2 if x>1 otherwise f(x)=-1
This is a function. Choose any value of x and the corresponding
y value will be 2 if x>1, or it will be -1 if x<=1
But each x value will have only one corresponding y value.
--------------------------------------------------------------
B. f(x)=5 if x>0 or f(x)=-5 if x<0 or f(x)=5 or -5 if x=0
Not a function because you have two points (0,5) and (0,-5)
Notice that x=0 has two associated y values, so not a function.
---------------------------------------------------------------
C. f(x)=x/10
This is a function; each x value has one y value associated with it.
=========================
Cheers,
Stan H.

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Domain requires that denominators must NOT equal zero! In this case, x canNOT equal 2 or -2. Domain therefore is all values of x except 2 and -2.
In interval notation: (-inf, -2) U (-2,2) U (2, inf).

R^2

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You have to state the problem. We don't have your book!!
R^2

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Slope is defined as:
m = (y2-y1)/(x2-x1)
.
So, if your two points are:
(-2.4,16.5) and 0.1,9.3)
then
m = (y2-y1)/(x2-x1)
m = (9.3-16.5)/(0.1-(-2.4))
m = (9.3-16.5)/(0.1+2.4)
m = (-7.2)/(2.5)
m = -2.88

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find the slope, if it exsists, of thel ine containing the pairt points.
(-2.4,16.5) and 0.1,9.3)
------------
The slope, m, = diff in y/diff in x
m = (9.3-16.5)/(0.1-(-2.4))
m = -7.2/2.5
m = -2.88

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Start with the given equation.


Subtract 4 from both sides.


Divide both sides by to isolate y.


Break up the fraction.


Divide


So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point

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log378= 2.5775
-------------------
5In(r) + 3In(t) - 4In(s)
= lnr^5 + lnt^3 - lns^4
= ln[r^5*t^3/s^4]
----------------------------

In(x) +In(x-2) = In(x+2) + In(x-3)
= ln[x(x-2)] = ln[(x+2)(x-3)]
x(x-2) = (x+2)(x-3)
x^2 - 2x = x^2 -x -6
x = 6
--------------------------------
g(x) = x^2+3 and h(x) = (x+ 3)/2

Find (h o g)(x) = h[x^2+3] = [(x^2+3)+3]/2 = [x^2+6]/2
===============================
Cheers,
Stan H.

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Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x.
--------------
f(x) = 2x^3 + 7x^2 -x-1
---
f(1) = 2 + 7 - 1 - 1 = 7 ; plot point (1,7)
----
f(2) = 2(2^3) + 7*2^2 -2 - 1
= 2*8 + 7*4 -3 = 16 + 28 - 3 = 41 ; plot point (2,41)
---
f(4) = 2(4^3) +7*4^2 - 4 - 1
= 2*64 + 7*16 - 5 = 235 ; plot point (4,235)
----
f(8) = 2(8^3) + 7(8^2) -8 - 1 = 1463 ; plot point (8,1463)
------
f(16) = 9967 ; plot point (16,9967)
------------------------------------

The function is increasing at a pregressively faster and faster pace
as x increases from one to 16.
=========================================
Cheers,
Stan H.

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f(x)=5x-3
f(1)=5*1-3
f(1)=5-3=2 ans.
f(2)=5*2-3
f(2)=10-3=7 ans.
f(4)=5*4-3
f(4)=20-3=17 ans.
f(8)=5*8-3
f(8)=40-3
f(8)=37 ans.
f(16)=5*16-3
f(16)=80-3
f(16)=77 ans.
------------------------
f(x)=x^2-3x+2
f(1)=1*2-3*1+2
f(1)=2-3+2
f(1)=4-3=1 ans.
f(2)=2^2-3*2+2
f(2)=4-6+2
f(2)=0 ans.
f(4)=4^2-3*4+2
f(4)=16-12+2
f(4)=6 ans.
f(8)=8^2-3*8+2
f(8)=64-24+2
f(8)=66-24=42 ans.
f(160=16^2-3*16+2
f(16)=256-48+2
f(16)=258-48=210 ans.

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First, congratulations on keeping your mind sharp by learning new (math) skills.
First, we'll do some of the evaluations:
Substitute x = 1:



Substitute x = 16:



Repeat the above proceess, substituting, in turn, x=2, x=4, x=8.
--------------
Substitute x = 1



---------------
Substitute x = 16:



Repeat the above process, substituting, in turn, x=2, x=4, x=8.
-----------------
Substitute x = 2:




Substitute x = 8:





Repeat the above prcess, substituting, in turn, x=1, x=4, x=16.
----------------------
To answer the second part of the question, it is probably best to graph each of the functions (Red: ), (Green: ), (Blue: ) and examine the graphs to determine their behaviour at each of the specified values of the independent variable (x=1, x=2, x=4, x=8, x=16).

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Well, you want to work out each function for each value of x so using f(x) = 10^x and g(x) = ln(x), you get:
f(1) = 10
f(2) = 100
f(4) = 10000
f(8) = 100000000
f(16) = 10000000000000000
g(1) = 0
g(2) = 0.69
g(4) = 1.39
g(8) = 2.08
g(16) = 2.77
So, 10^x increases faster the higher x is, but ln(x) increases at a slower rate the higher x goes. It also helps to understand that ln(2^x) = x*ln(2) as this relates all the answers for ln(x).

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In 1992, the life expectancy of males in a certain country was 61.7 years. In 1997, it was 64.5 years Let E express the life expectancy in year t and let t represent the number of years since 1992.
---------
You have two points of the form (t,E)
One is (0,61.7) ; this is the intercept for the equation.
-------------
The other is (5,64.5)
-------------------------
slope = (64.5 - 61.7)/(5-0) = 2.8/5 = 0.56
------
The linear function E(t) that fits the data is
E(t)=_0.56t+61.7
------------------
Use the function to predict the life expectancy of males in 2005.
E(13) = 0.56*13 + 61.7 = 68.98 years
========================================
Cheers,
Stan H.

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Does this problem have a question....we have the givens

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:
divide both sides by 3

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The domain of a function is the set of values for which the function is defined. Since produces a real number for any real number value of , in other words, is real for all real , the domain is the set of all real numbers.

Contrast this with . Since the value 1 would make the denominator be zero, is not defined at , so the domain here is all real numbers such that .

Consider . is not defined in the reals for any value of x that is negative, so the domain of is the set of all real numbers such that .

See?

Good luck and happy holidays.

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Let x = pounds of soybean meal
then
240-x = pounds of cornmeal
.
"amt of protein from soybean" + "amt of protein from cornmeal" = "desired amt of protein"
.12x + .06(240-x) = .08(240)
.12x + 14.4 - .06x = 19.2
.06x = 4.8
x = 80 pounds (soybean meal)
.
cornmeal:
240-x = 240-80 = 160 pounds

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Given f(x) = some function of x, to evaluate f(a), just substitute a for x whereever it occurs in the function and do the arithmetic. I presume D stands for domain, so since all of your values are integers, you don't have any excluded values in any of the stated domains.

Here's how to do the first one:
Given that and D = {reals}, find .



Do the rest of them the same way.

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FIND: f + g and f - g
f(x) = 7x^2+5 g(x)= x^2-13
===========================

f + g = f(x) + g(x)
f + g = 7x^2 + 5 + x^2 - 13
f + g = 8x^2 - 8
===========================
f - g = f(x) - g(x)
f - g = 7x^2 + 5 - (x^2 - 13)
f - g = 7x^2 - 5 - x + 13
f - g = 6x^2 + 8
Understand?

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verify that the function g(x)=(x-2)/5 is the inverse function of f(x)=5x+2.
----------------------------------------------------
f([g(x)] = f[(x-2)/5] = 5[(x-2)/5] + 2 = (x-2) + 2 = x
---------------
g[f(x)] = g[5x+2] = (5x+2-2)/5 = 5x/5 = x
===========================================
Therefore g and f are inverse to one another.
Cheers,
Stan H.

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Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100mph and train B is traveling at 120mph. Train A passes a station at 8:15A.M. If train B passes the same station at 8:30A.M., what time will train B catch up to train A?
----------------------
Train A DATA:
rate = 100 mph ; distance = x miles ; time = d/r = x/100 hrs
-------------------
Train B DATA:
rate = 120 mph ; distance = x miles ; time = d/r = x/120 hrs
-------------------
EQUATION:
time A - time B = (1/4) hr
x/100 - x/120 = 1/4
Multiply thru by 4 to get:
x/25 - x/30 = 1
30x - 25x = 25*30
5x = 25*30
x = 5*30 = 150 miles
-------------------------
Train A time = x/100 = 150/100 = 3/2 hr
8:15 + (3/2) hr = 9:45 A.M.

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Your answer is correct.
Congratulations.
Cheers,
Stan H.

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so we are looking for the range or the y coordinates for x={-2,0,2} and the equation x-2y=2---->y=(1/2)x-1
:
x=-2--->...-2-2y=2---->....-2y=4--->...y=-2
x=0---->...0-2y=2----->....-2y=2--->...y=-1
x=2---->...2-2y=2----->....-2y=0--->...y=0
:
so we have the coodinates (-2,-2),(0,-1),(2,0)
:

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this is an equation of a line...it has infinite solutions by itself...for instance if x is 1 then -3(1)+y=12--->y=15...so one order pair is (1,15)...you can do this for any x value.....the solutions are any point you can find on that line.
:
this graph only shows a partial of what this line looks like as both directions go on forever
:

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a. A person's height as a function of the person's age (from age 0 to 100)
Non-linear. Maybe sort of linear in the early years. But once you get through your teen years, your height by age flattens out. In fact, in later years you actually shrink. So non-linear.
b. The probability of getting into a car accident as a function of the speed at which you drive.
I would say non-linear here too. Speed is definitely a factor. Even more so if the independent variable is 'accidents causing death or serious injury'. But there are lots of 15 mph fender benders. I would say non-linear - but a lot more linear leaning than the first one
c. The time it takes you to get to work as a function the speed at which you drive
no-linear. those two valuse are inversely related.

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Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions. Explain your reasoning for a, b, and c.
a. f(x) = x + 5
b. f(x) = 3 if x>2 otherwise f(x) = -2
c. f(x) = 7 if x>0 or f(x) = -7 if x<0 or f(x) = 7 or -7 if x = 0
My solutions
a. Is a Function
b. Is a function
c. Is not a function because f(x) = 7 or -7 when x = 0 ?
---------------------------
Cheers,
Stan H.

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The way to look at this is that you're graphing
price on the y-axis and cups on the x-axis.
Each point on the graph is (x,y) = (cups,price)
The problem gives you
(50,1) and
(25,2)
Since the problem says the relation is linear,
write the general equation for a straight line
where
m = slope
b = y-intercept
Now plug in the given points one at a time
(1) and
(2)
Solve for and
Subtract (1) from (2)


Plug this back into (2)



So, the equation is
answer
check the answer
Does it pass through the given points?
(50,1)



(25,2)



OK
If the price is the equation says I'll sell
cups. I'd probably sell a lot more
When the price is $3, the equation says i'll sell
no cups because it's too expensive

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we have 2 points we will label then (P,C) (1,50) and (2,25) so lets find the slope....change in C over change in P
:
25-50/2-1=-25 which is the slope of our equation...now lets the point slope formula ...I am going to use point (2,25)
:
C-25=-25(P-2)
:
C-25=-25P+50
:

:
as you can see this can also be solved for P
:
divide all terms by -25
:

:

: