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 Brandon Offline Member I can't get enough*********   Name: Brandon Age: 30 Gender: Male Posts: 2,542 Join Date: January 6th 2009 College Algebra Questions - August 21st 2009, 08:03 PM I just got done with my first week of college, and I'm in a College Algebra math class. To finish off the week, the teacher gave us some work to do over the weekend, and I have a bunch of questions. Right now we're doing functions. So if this is something that you know well and can explain in a simplified manner, then that'd be a great help. The first problem that I'm having trouble with is this: f(x)= ((4x^2+1)/(x^3)) a. 2 b. -2 c. -x The objective of the problems are to "evaluate each function at the given values of the independent variable and simplify". For f(2) and f(-2), I came up with 15/4. For (-x), I came up with 3x-1...not confident in that answer at all. My second problem is in a graph, which I made here: http://img522.imageshack.us/img522/8898/graph1.png The x-intercepts are 1 and -3 and the y-intercept is -3. The bottom of the function starts at -4, just clarifying if that graph is too sloppy to understand. What I need to figure out is: a. the function's domain b. the function's range c. the x-intercepts d. the y-intercepts e. and the missing function values that are indicated by question marks: f(-2) = ? and f(2) = ? For the domain, I put {x|-3≤x≤1}, and for the range I put {y|y≥-4}, but I'm not confident in those answers. I don't understand e period, so how would I find the missing function values? The last question that I have for now is another graph that has me completely stumped. It looks like this: http://img32.imageshack.us/img32/2284/graph1k.png Again, I have to find the domain, range, x-intercept and y-intercept, and the missing function values that are indicated with a question mark from f(-1) = ? and f(3) = ? I'd appreciate your help VERY MUCH.
 <:3 )~ Offline squeak Average Joe***   Name: olivia Age: 28 Gender: Female Location: Across the Universe Posts: 195 Blog Entries: 2 Join Date: May 26th 2009 Re: College Algebra Questions - August 21st 2009, 08:20 PM I'll take a stab at it... f(x)=(4(2)²+1)/(2³) =(4*4+1)/8 ---> 2*2*2=8 =(16+1)/8 =17/8 f(x)= (4(-2)²+1)/-2³ = (4*4+1)/-8 =-17/8 f(x)=4(-x)²+1/(-x)³ =4x+1/-x = -4x+1/x On the first picture: I'm sorry. I just read what the roots were (x-intercepts) from this we get the equation (x-1)(x+3)=x²+2x-3 which is the parabola's equation. The domain (x-values) is...x has to be greater than or equal to -3 and and less than or equal to 1. x>-3 and x<1 1>x>3 is the domain {x|1>x>3} The range is y>3 {y|y>3} This second graph looks like an absolute value graph. The parent function for an absolute value is y=|x|. Say it's x=-1. y=|1| and y=|-1|. This results in a mirror image across the y-axis. So if you fold the graph it's identical on both sides. The equation of this graph is roughly y=|x|+1 (as it's shifted up one from the parent function with a vertex at 0,0) To find out the x-intercept look at the graph. Where does it intercept the x-axis? Nowhere. So there is no x-intercept. The y-intercept: Where does it intersect on the y-axis? That would be at (0,1) as you can see there. =) The domain is just where the x-values begin and where they end (in layman's terms). So, the x values begin at x>0 and continue on for infinity. So, x>0 is the domain. And in set notation: {x|x>0} The range is just where the y-values being and where they end. Well, the only point where there is even a valid y point is at y=1. So the range is y> 1 (as you can see, the values continue on from 1 to foreverrr thanks to that arrow) In set notation: {y|y>1} For the missing values you can refer to the picture OR plug and chug. I'll plug and chug. =) f(x)=|x|+1 =|-1|+1 =1+1 =2 f(x)=|3|+1 =|3|+1 =3+1 =4 I hope I could help and I apologize for any mistakes as I'm a little math rusty from the summer. PM me if you need any more help. =) Live and let live. Last edited by <:3 )~; August 21st 2009 at 08:50 PM.
Brandon Offline
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Re: College Algebra Questions - August 21st 2009, 09:47 PM

Quote:
 For the missing values you can refer to the picture OR plug and chug. I'll plug and chug. =) f(x)=|x|+1 =|-1|+1 =1+1 =2 f(x)=|3|+1 =|3|+1 =3+1 =4
Where did you get the -1 and the 3 in the absolute value signs? And how could I look at the picture and determine what replaces the question mark?

 <:3 )~ Offline squeak Average Joe***   Name: olivia Age: 28 Gender: Female Location: Across the Universe Posts: 195 Blog Entries: 2 Join Date: May 26th 2009 Re: College Algebra Questions - August 21st 2009, 09:48 PM Because if you slide over -3 on the x-axis and see what lies above it in y-axis terms, that would be your y value. Well, x=-1, x=3. That's the equation for the function so just plug them in and solve for y. =) Live and let live. Brandon Offline
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Re: College Algebra Questions - August 21st 2009, 11:10 PM

Quote:
 Because if you slide over -3 on the x-axis and see what lies above it in y-axis terms, that would be your y value. Well, x=-1, x=3. That's the equation for the function so just plug them in and solve for y. =)
Sorry, I still don't quite understand.

Quote:
 f(-2) = ? and f(2) = ?
For e, I have to find the missing values of the function f(-2) and f(2). Don't the -2 and 2 mean something because each graph problem, they have different numbers in the f(number).

 <:3 )~ Offline squeak Average Joe***   Name: olivia Age: 28 Gender: Female Location: Across the Universe Posts: 195 Blog Entries: 2 Join Date: May 26th 2009 Re: College Algebra Questions - August 22nd 2009, 02:45 AM Oh okay. To find -2 and 2 plug and chug. Plug in the number and solve! f(x)=|x|+1 x=-2 f(x)=|-2|+1 =2+1 =3 f(x)=|x|+1 x=2 f(x)=|2|+1 f(x)=3 Basically it's showing how the absolute value symbol creates a graph that is symmetric on the y-axis. Also I would like to add this information: f(x) mean the function of x. y is a function of x. Which means it changes as x changes basically. f(x)=y Okay, on the thing you don't understand - remember plotting points? Slide over -3 on the x-axis and plot the first point you see on the function itself with a y coordinate by scaling your pencil upward vertically. Like that. =) Live and let live. Last edited by <:3 )~; August 22nd 2009 at 02:56 AM.
Brandon Offline
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*********

Name: Brandon
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Re: College Algebra Questions - August 22nd 2009, 04:32 AM

Quote:
 Originally Posted by <:3 )~ Oh okay. To find -2 and 2 plug and chug. Plug in the number and solve! f(x)=|x|+1 x=-2 f(x)=|-2|+1 =2+1 =3 f(x)=|x|+1 x=2 f(x)=|2|+1 f(x)=3 Basically it's showing how the absolute value symbol creates a graph that is symmetric on the y-axis. Also I would like to add this information: f(x) mean the function of x. y is a function of x. Which means it changes as x changes basically. f(x)=y Okay, on the thing you don't understand - remember plotting points? Slide over -3 on the x-axis and plot the first point you see on the function itself with a y coordinate by scaling your pencil upward vertically. Like that. =)

I figured it out, but in a different way. I'm good from here on. Thanks for your help though.

 <:3 )~ Offline squeak Average Joe***   Name: olivia Age: 28 Gender: Female Location: Across the Universe Posts: 195 Blog Entries: 2 Join Date: May 26th 2009 Re: College Algebra Questions - August 22nd 2009, 07:09 PM No problem! I'm glad that you figured it out. It's kinda difficult to explain it in text and not be showing somebody it. Best of luck in that algebra class x Live and let live. Tags algebra, college, questions Thread Tools Search this Thread Show Printable Version Email this Page Search this Thread: Advanced Search Rate This Thread Rate This Thread: 5 : Excellent 4 : Good 3 : Average 2 : Bad 1 : Terrible Posting Rules You may post new threads You may post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are Off Refbacks are Off Forum Rules