Functions, Notation checking if i did these correct

zee-f · 2011-09-04 07:31:34

13. Find the domain of

A. x ≠ 1

B. x ≠ -1, 0, 1

C. x ≠ 0

D. x ≠ -1,1

E. x ≠ -1

F. x ≠ -2

14. Find the domain of

A. x ≠ -1

B. x ≠ 1

C. x ≠ -2

D. x ≠ -1, 1

E. x ≠ 2

F. x ≠ 0

15. Find the domain of

A. x ≠ -1

B. x ≠ 0

C. x ≠ 1

D. x ≠ 4

E. x ≠ -2

F. x ≠ -1, 1

16. Find the domain of

A. x ≠ 4

B. x ≠ 6, -1

C. x ≠ -4

D. x ≠ -6, -1

E. x ≠ -2, -3

F. x ≠ 2, 3

Last edited by zee-f (2011-09-04 07:35:46)

anonimnystefy · 2011-09-04 07:38:11

again your solutions are correct.

i am glad you learned LaTeX!

Bob · 2011-09-04 07:40:12

hi zee-f

Yes, so am I. That's so much clearer. And I'm happy with all of these too.

Are you ok with (11) now?

Bob

Last edited by Bob (2011-09-04 07:42:05)

zee-f · 2011-09-04 07:45:33

yup i am thanx allot but i have a question like the domain for 13 is all real numbers except -1 so is it right to answer the question with x ≠ -1 like when i solved for x i got -1 so why do we sayx ≠ -1

zee-f · 2011-09-04 07:46:58

thanx anonimnystefy am happy i learned LaTeX to its much clearer

Bob · 2011-09-04 07:54:46

hi zee-f

For a function like

you can put in any value of x without a problem.

so

But if there's a value that cannot be allowed it has to be excluded by putting x ≠ that value or values.

In all your functions 13 to 16, there's a denominator which can be zero. That means the overall function zooms off to infinity and that's not allowed. So finding when the denominator is zero gives a possible exclusion.

eg.

The denominator is zero when x = 3 or -3 so they're the values to exclude with x ≠ 3 and x ≠ -3.

Notice it doesn't matter when the numerator is zero. Put x = 2 or -2 and the top of the function is zero, so it is zero overall. That's allowed because zero is a number unlike infinity.

Does that clear it up?

I'm just making a graph as well for this so stay on-line a moment longer.

Bob

Last edited by Bob (2011-09-04 07:56:47)

zee-f · 2011-09-04 08:02:24

yup its pretty clear and ok thanx allllllot

Bob · 2011-09-04 08:03:42

Ok here it is.

This is the graph for the function I made up in my last post.

You should be able to see that the line crosses the x axis at x = -2 and x = + 2. That's where y = 0. This is OK.

But look what happens to the graph at x = -3 and x = + 3. Can you see what I mean by zooming off to infinity. It doesn't matter what scales you use, you can never get to the 'top' of the curve. It just goes up and up (or down and down to minus infinity)

Bob

zee-f · 2011-09-04 08:32:15

thats pretty helpful and clearer u made my day thank you sooo soooooo much

zee-f · 2011-09-04 08:41:57

i got number one incorrect i answered it as d any clue why ??

bobbym · 2011-09-04 10:40:04

Hi zee-f;

D is correct. It is not a function. The last number does not map to anything. What does she think is the answer?

Bob · 2011-09-04 19:58:37

hi zee-f,

When I first looked at (1), I thought C, because every element goes to just one number. But then I thought about it properly and realised that your answer of D was the correct one because there is no definition for where -3 goes.

To be a function the rule must be 'well defined'. That means you must always know where each number goes and we are not told where -3 goes.

Stick to your answer; both bobbym and I think it's correct. Ask your teacher to consider what we've said and let us know what happens.

Oh just one other possibilty. Are your images the right way round in that post? I'm pretty sure that's not the explanation though, because the alternative answers wouldn't make sense if the images were reversed.

Bob

bobbym · 2011-09-04 20:24:12

Hello bob bundy;

Whoa! Did you do it now. Her teacher is a toughie.

Hi zee-f;

Hope you read the above comments. The great thing about mathematics is sometimes you just know you are right. If you did the calculation then you have to stand up for what you know is true. Politely of course, you have to convince her you are right.

zee-f · 2011-09-04 21:14:40

hi bob bundy and bobbym,

am pretty sure my answer is correct am ganna discuss with my teacher see what she thinks is correct

bobbym · 2011-09-04 23:20:35

Hi;

Please let us know what she says.

zee-f · 2011-09-05 03:01:58

hey ,

i got a reply from her
#1. The correct answer is A, there are more numbers in the domain, which causes -3 not to map to anything, but I accept D also.

i got a 10 in that lesson thank you guyssss sooooooo much

bobbym · 2011-09-05 03:07:44

Hi zee-f;

I do not agree with two answers there. As long as she did not mark you wrong.

Very good work!

Bob · 2011-09-05 03:44:35

hi zee-f and bobbym,

A function may have more numbers in the domain than in the range. For example in question 6 where all the domain values map onto the single number 1.

But a function must be well defined meaning that every number in the domain must map somewhere.

D is the correct answer. A is not.

I think you deserve this for getting right a question your teacher could not do:

Bob

Last edited by Bob (2011-09-05 03:45:43)

bobbym · 2011-09-05 15:27:18

Hi all;

Of course she is wrong to say that she will accept D. D is the correct answer. D does not have beg his way to the top. D is the champ!

This is the third question she has made a mistake on. That is not terminal, expecting people to be perfect is unrealistic. I would be happier if she were a little more flexible in her attitudes when she wrong.

Bob · 2011-09-05 20:35:30

hi bobbym,

It goes with the job. Teachers spend all that time telling others what to do and being 'knowledgeable' so two things make teachers in-secure:

(i) Having someone in the class who is more intelligent than they are;

(ii) Being found out for having made a mistake.

So the defences come up and the teacher tries to maintain black is white rather than admitting the error.

Of course, none of this applies to me, does it?

I have to admit, I was horrible to some of my teachers:

the chemistry teacher who accidentally called water an element and was questioned about all the electrolosis etc that varies the amount and then asked to prove everything

the teacher who insisted a prism with a parallelogram cross-section was a parallelopiped (well yes it is in the strict definition but this teacher wouldn't accept that their model was just a special case rather than a good example of the general class)

the physics teacher who had to be shown how to get from the differential equation for a charging circuit to the equation

etc etc.

So I hope I'm wiser for all that. If a student points out a mistake, I just say "Oh yes, well done, I hadn't thought of that. Thanks."

But you need to feel secure first. Maybe this should be a part of teacher training.

Bob

bobbym · 2011-09-05 20:51:10

Hi;

I have to admit, I was horrible to some of my teachers:

You were horrible to them?!
I wake up in a cold sweat sometimes thinking that some of them might come looking for me.

Of course, none of this applies to me, does it?

No.

zee-f · 2011-09-08 05:22:51

thank you alllllllllll

bobbym · 2011-09-08 05:35:36

Hi zee-f;

You are welcome! How are you today?

zee-f · 2011-09-08 23:13:10

am great how are u doing bobbym

bobbym · 2011-09-08 23:31:58

Not so good, I have lots of problems that I am working on and not getting anywhere.

Math Is Fun Forum

#26 2011-09-04 07:31:34

Re: Functions, Notation checking if i did these correct

#27 2011-09-04 07:38:11

Re: Functions, Notation checking if i did these correct

#28 2011-09-04 07:40:12

Re: Functions, Notation checking if i did these correct

#29 2011-09-04 07:45:33

Re: Functions, Notation checking if i did these correct

#30 2011-09-04 07:46:58

Re: Functions, Notation checking if i did these correct

#31 2011-09-04 07:54:46

Re: Functions, Notation checking if i did these correct

#32 2011-09-04 08:02:24

Re: Functions, Notation checking if i did these correct

#33 2011-09-04 08:03:42

Re: Functions, Notation checking if i did these correct

#34 2011-09-04 08:32:15

Re: Functions, Notation checking if i did these correct

#35 2011-09-04 08:41:57

Re: Functions, Notation checking if i did these correct

#36 2011-09-04 10:40:04

Re: Functions, Notation checking if i did these correct

#37 2011-09-04 19:58:37

Re: Functions, Notation checking if i did these correct

#38 2011-09-04 20:24:12

Re: Functions, Notation checking if i did these correct

#39 2011-09-04 21:14:40

Re: Functions, Notation checking if i did these correct

#40 2011-09-04 23:20:35

Re: Functions, Notation checking if i did these correct

#41 2011-09-05 03:01:58

Re: Functions, Notation checking if i did these correct

#42 2011-09-05 03:07:44

Re: Functions, Notation checking if i did these correct

#43 2011-09-05 03:44:35

Re: Functions, Notation checking if i did these correct

#44 2011-09-05 15:27:18

Re: Functions, Notation checking if i did these correct

#45 2011-09-05 20:35:30

Re: Functions, Notation checking if i did these correct

#46 2011-09-05 20:51:10

Re: Functions, Notation checking if i did these correct

#47 2011-09-08 05:22:51

Re: Functions, Notation checking if i did these correct

#48 2011-09-08 05:35:36

Re: Functions, Notation checking if i did these correct

#49 2011-09-08 23:13:10

Re: Functions, Notation checking if i did these correct

#50 2011-09-08 23:31:58

Re: Functions, Notation checking if i did these correct

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