







The domain and range of a function 
20160219 

From Genius: State the domain and range
g(x)=x(x1) Answered by Penny Nom. 





The range of a function with a finite domain 
20160125 

From Hannah: Solve y=(1⁄4)x1 if the domain is (4,2,0,2,4).
I don't get how to do this. Can anyone help? Answered by Penny Nom. 





Fractions of two quantities 
20160122 

From Melody: Kate ate 1/4 of her orange. Ben ate 2/4 of his banana. Did Kate and Ben eat 3/4 of theit fruit? Explain. Answered by Penny Nom. 





The range of a function defined piecewise 
20160113 

From sarah:
f(x)={x2, x<2
{x^24, 2_<x_<2
{x+2, x>2
find the range Answered by Penny Nom. 





The range of f(x)=(2x+2)/(x1) 
20151125 

From Nazrul: f : R to R is a function which is defined by f(x)=(2x+2)/(x1).
Is f(x) an onto function? Please explain.
What is the range of this function?
Thank you very much for your previous help. Answered by Harley Weston. 





Arrangements of the letters STRANGE 
20150822 

From Ravi: In how many ways can the letters of the word STRANGE be arranged to that the vowels occupy only the old places. Answered by Penny Nom. 





A quadratic equation 
20131127 

From corinanna: Hi,
How do you find a quadratic equation given the domain & range,
& or the yintercept? Answered by Penny Nom. 





How many oranges? 
20121006 

From Rodger:
Question from Rodger, a teacher:
How Many Oranges?
Marjorie, Colleen, and Bob picked oranges together. They were tired after picking a large number of oranges and so fell asleep. Marjorie woke first and decided to take her third of the oranges and head home. She counted the oranges, and found that the number was divisible by 3 if she took one of the oranges first. Marjorie took one orange and then took onethird of the remaining oranges. She left quietly.
Bob awoke a short time later, noticed that Colleen was sleeping, and presumed Marjorie had gone for a walk. He decided to head home because he wasn't feeling well. Not realizing that anyone had left, he counted the oranges and found that the number of oranges was two more than a number that could be easily divided by 3. So he took the two extra oranges and then onethird of what was left. He left without waking Colleen and without waiting for Marjorie to return.
Colleen finally awoke and wondered where her friends had gone. She assumed they were both busy somewhere nearby. Before she left, she counted the oranges and was surprised at how small the number was. She found that the number of oranges was one more than a multiple of three, so she took the extra orange and one third of those remaining.
1. What was the total number of oranges the friends picked?
2. How many oranges were left behind when Colleen departed?
3. Is more than one answer possible for the total number of oranges? If so, what other numbers are possible? Explain.
4. Based on the values you found in problem 3, determine a reasonable solution to the problem. Explain your answer.
5. Is it possible that five oranges remained after Colleen took her share? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern
5. Is it possible that five oranges remained after Colleen took her “share”? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern Answered by Penny Nom. 





The range in grouped data 
20120827 

From maria: Question from maria, a student:
how to find range from group data.?i know that it is the difference between largest and smallest value.but confuse to find range of group data e.g
class interval 
frequency 
05 
6 
510 
7 
1015 
9 
1520 
4 
Answered by Robert Dawson. 





The range of h(x) = 1/x 
20120811 

From Lucy: What is the range of the function: h(x)=1/x (and can you please explain why)? Answered by Penny Nom. 





Domain and range 
20120809 

From Lucy: Can two different functions have the same domain and range? Why or why not? Answered by Penny Nom. 





The same mean but different ranges 
20120114 

From swathi: Frank and Frances work out at their local gym. the mean of their workout times is the same: 48 min. however, the range of Frank's workout times is 7 min, while the range of Frances'sworkout times is 16 min. explain how this is possible. Answered by Penny Nom. 





In how many ways can 12 members of volleyball team line up ... 
20111118 

From Aatir: In how many ways can 12 members of volleyball team line up if the captain and assistant captain have to remain together. Answered by Penny Nom and Stephen La Rocque. 





Building a custom range hood 
20111008 

From Bill: I'm building a custom range hood for a customer with special order material that matches
their newly installed cabinets and I need it to be perfect. The hood is basically a pyramid
but the 4th side is the flat wall at the back and a flat, rectangular top. I need to calculate
the bevel and miter of the three sides but I never was very good with geometry functions
(although I am fairly good with other math fields). I either need the calculations from you
at least (shudder) a formula or set of formulas so that I can calculate them myself. Answered by Harley Weston. 





Arrangements of ten letters 
20110415 

From Mustafa: In how many ways can the ten letters of the word GELATINOUS be arranged
in a line so that the vowels are in alphabetical order (not necessarily together)
when read from left to right? Answered by Penny Nom. 





Rearrange for x 
20110206 

From sue: (x+7)/3 = (3xy+2x)/4 rearrange for x Answered by Penny Nom. 





A box full of oranges 
20101028 

From Mary: A box full of oranges weighs 9 pounds. After a family ate 2/3 of the oranges, the remaining oranges and the box weighed 4 pounds. The weight of the box when empty is how many pounds? Answered by Penny Nom. 





The domain, range and inverse of a relation 
20100108 

From Nazrul: Given that A={2,1,0,1,2}, S={(x,y): x belongs to A, y belongs to A and y^2=x}. How can I find the domain and range of the relation S. What is the inverse relation of S. Please show me the process in details.
Thank you. Answered by Penny Nom. 





y = sin(x) + 3 
20091110 

From Kapilan: When graphing trigonometric functions like SIN and COSINE does f(x)=x
squared equal to SIN or COSINE
Also what is the range, domain, period and ampliltude for y=sin@ + 3 Answered by Harley Weston. 





Probability 
20090927 

From Ed: My mother died 3 years to the day after her daughter died. what are the odds of that happening by chance? thanks Answered by Chris Fisher. 





Domain and range 
20090911 

From Aubrey: I'm supposed to "state the domain/range of each of the following relations" and it's totally not making sense...
Examples:
{(x,y) : x = square root of y}
{(x,y) : y = x + 1, x is some even integer}
Thanks in advance!!
Aubrey Answered by Robert Dawson. 





Arrangements 
20090820 

From Anna: How many arrangements of FATHER can be made if all the vowels must be kept together? Answered by Leeanne Boehm. 





Rearrangements of 8028842 
20090717 

From Con: How many different 7digit numbers can be made by rearranging the digits in the number 8028842? Answered by Penny Nom. 





Range and Domain of a Star 
20090514 

From Larry: I am an old teacher trying to help my grandson. He has to draw a structure to scale and then determine the function, domain and range. One line on the structure is from (0,8) to (8,4). I used the intercept method and found the function to by y=1.5x +8 (I think) but can't find the range and domain) Thanks Answered by Janice Cotcher. 





0123456789 
20090325 

From Dr.: Many years ago I discovered that there are 33 numbers which,
when multiplied by 0123456789, simply rearrange the digits. Surprisingly
(to me at least) is the fact that the digits of all of those 33 numbers add up
to one of the 6 "cardinal" numbers 1, 2, 4, 5, 7, and 8. For example
6 + 2 = 8 and 62 X 0123456789 = 7654320918 etc.
Another interesting (to me) fact is that only the cardinal numbers
1, 2, 4, 5, 7, and 8 rearrange the digits in the number 9876543210.
My question is: "Is this known to anyone but me and the people I have
told?" Answered by Robert Dawson. 





Seating 8 people in a row 
20090215 

From raymond: In how many ways can 4 boys and 4 girls be seated in a row if they may sit anywhere Answered by Penny Nom. 





4 digit arrangements of 7 3 6 6 
20090205 

From Carole: I need all the four digit combinations using the numbers 7 3 6 6 Answered by Penny Nom. 





The range of a set of numbers 
20081119 

From krista: hi, i was working on a math problem for homework and it asked me to
find the range out of these numbers:
1,15,16,16,19,25,27,28,28, can you help me? Answered by Penny Nom. 





Domain and range 
20080916 

From Cara: Please help me to find the domain and range of the following function:
F(x)=sin(2x) Answered by Harley Weston. 





The range of a dataset 
20080727 

From Todd: When calculating the range you subtract the low number from the high number. If all the scores are the same is the range considered 1 or 0? Answered by Stephen La Rocque. 





Domain and range 
20080723 

From Cane: Hi, my name is Cane and i am stuck on this problem. Find the doman and
range then graph.
y= square root of(x squared  6x) + Square root of(6x  x squared) Answered by Harley Weston. 





The maximum range of a projectile 
20080722 

From kwame: the range R of projectile fired with an initial velocity Vo ,at an angle of elevation (@ )theta from the horizontal is given by the equation R = (Vo(squared) sin2theta)/g. where g is the accelation due to gravity . Find the angle theta such that the projectile has maximum range . Answered by Harley Weston. 





Domain & Range of a Periodic Function 
20080711 

From Michelle: The depth, w metres, of water in a lake can be modelled by the function,
w=5sin(31.5n+63) +12 where n is the number of months since
January 1, 1995. Identify and explain the restrictions on the domain and
range of this function. Answered by Janice Cotcher. 





Smallest Even Number 
20080709 

From Ma.: Using the digits 0, 1, 3, 4, and 5 only once give the smallest 5digit even number Answered by Janice Cotcher. 





Domain and range 
20080707 

From marylie: what is the domain and range of f(x)= sq.rootof x ^24??tnx Answered by Harley Weston. 





Escort cards on a rectangular table 
20080613 

From Susan: What size rectangular table will we need to put 230 2" X 3.5" escort cards on for my daughter's wedding reception with a spacing of .5 inch between them on all sides? Thanks so much for your help Answered by Penny Nom. 





How many different ways can cards fall when shuffling? 
20080609 

From Twyla: How many different ways can cards fall when shuffling? In other words,
if you have 52 numbers, each one unique, how many different ways can
they be arranged, using each number only once? Answered by Penny Nom. 





Rearrangements of the digits in 0123456789 
20080323 

From Joe: Found a close problem but not quite.
Using digits 0123456789, how can I figure what all the different
possibilities would be without repeating any digits?
I know that there are 10! possible answers but how can I figure out what
they are? Answered by Stephen La Rocque. 





Percent and range 
20080306 

From Greg: How do you find out the percent of a number that is with in a range of numbers (i.e. what % is 39 of range 34 to 42)? Answered by Penny Nom. 





All possible arrangements of the word "PROBLEM" 
20080225 

From student: Consider all possible arrangements of the word "PROBLEM". If a word is picked at random, find the probability that
(a) the word starts with a vowel
(b) the word ends with a consonant. Answered by Harley Weston. 





The range of a function 
20080210 

From Rachel: How do I find the range of this function?
(3x^32x^2+6x7)/(x^23x4) Answered by Harley Weston. 





The domain and range of a function 
20080205 

From Victoria: Please...Please...Please tell me how to find domain and range.
Every text and website i have gone to does not make any sense to me!
Below are two example problems i found on a website...
f(x) = (8x3)/(4x1)
and
y = 2x+1
Please explain step by step how to find the domain and range. Answered by Penny Nom. 





Range of a Function 
20080115 

From Amanda: I'm studying for the midterm and I can't seem to grasp this one question on my review sheet. Can you help me?
Find the range of a function y = 32 + 5x where 0 < x < 8 and x is an integer. Answered by Penny Nom. 





Percent change between two value ranges 
20071128 

From Joe: How do you calculate a percent change between tow value ranges  for instance if I project a range for 2007 to be between 100 and 120 and a range for 2008 to be between 120 and 140, how do I calculate the estimated increase between the range? Is it 0% to 40% (taking the two inside values rto calculate the minimum and the two outside values rto calculate the maximum?) Answered by Harley Weston. 





The range of a function 
20071112 

From Camille: Hi There,
I am taking a calculus class by correspondence and part of the introduction is
learning how to find domain and range of functions. I understand how to find the
domain. I also understand that if you find the inverse of the equation and
solve for x to find the domain it will give you the range because the domain
of the inverse is equivalent to the range of the original equation. However when
trying to apply this method to complicated questions (ie: square root in the
denominator) I get confused and can't solve for x.
Camille Answered by Harley Weston. 





Stem & Leaf Plots 
20071102 

From Jen: Trying to help my Gr.4 son with his math and i am a little lost here are the
stem and leaf plots..
Stem Leaves
4 02
3 1226699
2 011255789
1 33357899
Stem Leaves
2 00011111223334455
1 range566788899
Question  How are the ranges for the stem & leaf plots different ? Answered by Penny Nom. 





Domain and range 
20071012 

From Dawn: Hi, I've been out of school for 8 years and recently picked up a math correspondence course. I'm having trouble trying to figure out the range and domain of a linear function. I've read everything I can find in my text, lessons and on your site and I still can't figure out what I'm suppose to be doing. The function is y=2x+1. Please help. Answered by Penny Nom. 





Arrangements of children by age 
20070902 

From shani: How many different arrangements of children by age can there be in families with four children?(hint: Boygirlboygirl is different from boygirlgirlboy. Presume there are no twins)
The hint is more confusing than the question. Answered by Penny Nom. 





Rearranging the alphabet 
20070818 

From samhita: Find the number of ways of arranging 26 letters in the English alphabet in a row such that there are exactly 5 letters between x and y. Answered by Stephen La Rocque and Penny Nom. 





The domain and range of a quadratic function 
20070717 

From Linda: I have been trying to solve this problem but I'm unable to figure it out. How do I find the domain and range of
y=(x+1)^23? Please explain...thanks! Answered by Stephen La Rocque and Penny Nom. 





Interval of the domain 
20070513 

From Gale: What does the term interval of the domain mean? Answered by Penny Nom and Stephen La Rocque. 





A missing observation 
20070402 

From destinee: please help me my problem is 5,11,19,3,15,17,5,n find n given the following info.range:16 mode:5 median:8 mean:10 what the heck is the answer Answered by Penny Nom. 





Range in statistics 
20070228 

From Steve: I was wondering if the range is considered as a positive or negative number, or does it ignore such indications? Answered by Penny Nom. 





Inputoutput table 
20070110 

From Richard: Question is make an input  output table for the function using the domain 0,1,2,3,4, Then state the range of the function.
y =x + 8 ?
y =0.4x +3 ? Answered by Penny Nom. 





How many arrangements are there? 
20060416 

From Jim: Can you tell me how many different combinations there are using 3 letters and 4 numbers. Letters first then numbers, example aaa0001, aaa0002, aaa0003,baa0001, baa0002, zzz9999. Answered by Stephen La Rocque. 





Domain and range 
20060308 

From Jennifer: How do I find the domain of x2y=1 if the range is {2,0,5,8} Answered by Penny Nom. 





The range of a data set 
20051004 

From Carmen: What is the range of this data? 36,64,37,45,53,60. Answered by Penny Nom. 





The range of a function 
20050821 

From Kelsey: What is the range of the function f(x) = 4x  6 when the domain is {3,1,1,3,5}? Answered by Penny Nom. 





A seating arrangement 
20050203 

From Kay: If you have 5 married couples, how many arrangements can be made if they must sit across from each other? Answered by Penny Nom. 





Domain and range 
20040801 

From JJ: I'm checking domain and ranges of these functions. Are these right? Answered by Penny Nom. 





Two Problems 
20040712 

From Justina: i cant figure out the range of this equation in interval form because the highest point seems to be a decimal. please help f(x) = x + sqrt(4x2)
.............................................................................
Building Design A circular air duct of diameter D is fit firmly into the rightangle corner where a basement wall meets the floor (see figure). Find the diameter of the largest water pipe that can be run in the rightangle corner behind the air duct. Answered by Claude Tardif and Penny Nom. 





Rearranging an expression 
20040224 

From Corey:
use the following formula to answer the question
F=9c divided by 5 plus 32
rearange the formula to solve for c
how many degrees fahrenheit would it be it it was:
0 degrees celcius
10 degrees celcius
46 degrees celcius
Answered by Penny Nom. 





Arrangements around a circular table 
20031007 

From Lori: How many arrangements can 6 people be seated round a circular table? Answered by Penny Nom. 





The domain of 1/g(x)  5 
20030703 

From Barbara: If the range of g(x) is ( neg. infinity,4] and the domain of g(x) is ( neg. infinity, infinity), how do I find the domain of 1/g(x)  5? Answered by Penny Nom. 





Runs 
20030316 

From Diana: How many arrangements are there with n 0's and m 1's, with k runs of 0's? (A run is a consecutive set [1 or more] of the same digit; eg. 000 111 0 11 00 has three runs.) Answered by Penny Nom. 





Functions and relations 
20020425 

From Erin: Here's a few math problems that might drive a person insane ;)  If 2f(x)  3f(1/x) = x^2 what is f(2)?
 What are the domain and range of the following relations?
 x^2  4y^2 = 25
 4x^2 + 9y^2 = 36
 The port of Swan Harbor is 200km away from Merry Town Inlet on a bearing of N50E from Merry Town. A ship leaves Merry Town at 8am and sails N15W at 15 km/h. At the same time, a second ship leaves Swan Harbour on a course of S80W at 20km/hour. How close, to the nearest km, are the two ships at 13:00?
 Prove the identity. 1+sinx + cosx/ 1sinx + cosx = 1+sinx / cosx
Answered by Penny Nom. 





Composition of functions 
20020406 

From Yvonne: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = x^{2}  4 and g(x) = sqrt(x) The range of f(x), x<=4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(x^{2}  4). In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything? Answered by Claude Tardif. 





Tonya in the orange grove 
20010425 

From A parent: Tonya was helping in the orange grove. She decided to take some oranges home to share with 3 friends. She gave 3 more than half to Jennifer. Angela got half the remainder and 3 more. She gave Josie half the remainder plus three. When she got home, she had only 10 oranges left. How many did she have when she left the grove? Answered by Penny Nom. 





Domain and Range and Zeros 
20010227 

From Beth: 1. f(x)=152xx^{2} 2. g(t)=square root of 4t^{2} 3. y=t3/t^{2}t6 Answered by Penny Nom. 





Arranging some numbers 
20010114 

From Denise: Arrange the following numerals in two groups of four each so that each group will add to give the same sum. 1 2 3 4 5 7 8 9 Answered by Penny Nom anf Claude Tardif. 





What is the difference between Mean and Average? 
20001213 

From Julie: What is the difference between Mean and Average? My thinking is the average, is the equal to the sum of all numbers divided by the number of numbers added together. But the mean, I think should be calculated by adding the largest and smallest numbers in the set and them dividing by 2. (which is the point where 1/2 the numbers are higher and 1/2 the numbers are lower) Answered by Patrick Maidorn and Penny Nom. 





Range of a function 
20001121 

From David Bell: Given a rational function such as f(x) = (8x3)/(4x1). How can the range be found. Answered by Penny Nom. 





Calculator and telephones keypads phones 
20000627 

From Thomas Smith and Veronica YatesRiley: On a keyboard, why is the number "7" on the top of the keypad as opposed to the number "1" at the top a telephone keypad? Answered by Penny Nom. 





Approximations 
19991220 

From Adrian Valc: Longtime ago I red an article about surprizing (and in a way frustrating) results in math, for example the limit of a nicely defined infinite series which was believed to be a simple rational number, but later was determined to be a transcendent number that missed the rational value by an incredibly small amount (so for example the limit proved to be 2.75000...00137.. with a lot of 0's in between). I cannot find that article anymore, so i was wondering if you have any such examples, or you can point to any relevant information source? Answered by Chris Fisher. 





Domain and Range of a Function 
19991114 

From Michelle Mellott: How do you find the range of the following function: 2y^{2}/(y^{2}+5y+6)?? I know the domain is x not equalled to 2, 3. How can one easily find the range? Answered by Harley Weston. 





The Range of a Function. 
19970912 

From Karel Marek: Math Is Book 6 (Ebos/Tuck) question 5(b) gives a surprising answer at the back of the book..The question is: Indicate the domain and range for this: y = sqr(x9) (Square root of) The answer for the domain is x>=9 which is not surprisingly, but the range is y>=0, yER ... which I could understand if you were not allowed to transform the equation into x as the subject.. But all example on the facing page DO TRANSFORM the equation at will with x and/or y as the subject.. Can you explain this... ?? Answered by Chris Fisher. 

