anonymous
  • anonymous
Why is this a horizontal translation of 10 from looking at the graph?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1332600010376:dw|
anonymous
  • anonymous
|dw:1332600070206:dw|
anonymous
  • anonymous
The equations are: C(x) = 20/(50+x) C(x) = 20/(40+x)

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anonymous
  • anonymous
Perhaps a better graph would help? http://www.wolframalpha.com/input/?i=y+%3D+20%2F%2850%2Bx%29++and+y%3D20%2F%2840%2Bx%29 Notice the pink graph (20/(40+x)) has been shifted 10 units to the right, relative to the blue graph (the first equation above).
anonymous
  • anonymous
ohh, sorry D: How is it shifted 10 units to the right?
anonymous
  • anonymous
One way to look at it is in terms of the vertical asymptotes. We can't divide by zero, so the vertical asymptote is x=-50 for the first graph. It is x=-40 in the second graph. -40 is ten units to the right of -50...so the entire graph is moved 10 units to the right, as shown in the graph.
anonymous
  • anonymous
hmm.. where is the vertical asymptote
anonymous
  • anonymous
They are shown on the link I gave you as the vertical blue line (for the first equation), and the vertical pink line (for the second equation).
anonymous
  • anonymous
the asymptote is like the line that does not touch zero, correct?
anonymous
  • anonymous
An asymptote is a line that your graph gets closer and closer to but never touches or crosses it.
anonymous
  • anonymous
ohhh, so for the blue line it's on the x=-50, btw do you know the scale for this graph?
anonymous
  • anonymous
brb
anonymous
  • anonymous
okay
anonymous
  • anonymous
Correct. The graphs are shown with two scales. The top one is shown x from -50 to -40, the bottom pic (much better) shows x from -20 to -70. y is between 0 and about 6.5 on the bottom one
anonymous
  • anonymous
do you know how I can graph this onto my graphing calculator (TI-83+)? Because I didn't get the same graph o.o
anonymous
  • anonymous
well, you need to type in the equation correctly for y1 and y2 in your calculator. Make sure you use brackets for the denominators or you're graphing the wrong equations. Then you need to set your viewing ranges for x and y. Use x from -20 to -70 and y from -7 to +7
anonymous
  • anonymous
not sure how to set the viewing rectangle on your TI83
anonymous
  • anonymous
why x -20 to -70 and y from -7 to 7?
anonymous
  • anonymous
It gives you a better picture of what is happening. It's the viewing rectangle for the bottom picture on the link I gave you
anonymous
  • anonymous
ohh, but say this was on the test how would you know what to set?
anonymous
  • anonymous
trial and error more or less.
anonymous
  • anonymous
you need to see the graph as well as you can. you dont need to graph these to kknow it is a horizontal translation of 10 units right. your equations tell you this
anonymous
  • anonymous
ooh. Really?? How does it tell me?
anonymous
  • anonymous
suppose you have a function f(x). A function f(x+a) is the same as f(x) only translated a units to the left. f(x-a) is f(x) translated a units to the right.
anonymous
  • anonymous
example: f(x)=2x+1 shift 3 units left: f(x)=2(x-3)+1
anonymous
  • anonymous
ooops...shift 3 units left is f(x)=2(x+3)+1 watch your signs!
anonymous
  • anonymous
ohh, i see. But how do I read C(x) = 20/(50+x)?
anonymous
  • anonymous
so C(x)=20/(50+x) now let's shift it 10 units to the right (we will need to subtract 10 units to do this): So, your shifted function is: C(x)=20/(x-10+50)=20/(x+40)
anonymous
  • anonymous
but what if I don't know that i need to shift 10 units to the right? I'm so sorry for asking so much questions D:

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