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The equations are: C(x) = 20/(50+x) C(x) = 20/(40+x)
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).
ohh, sorry D: How is it shifted 10 units to the right?
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.
hmm.. where is the vertical asymptote
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).
the asymptote is like the line that does not touch zero, correct?
An asymptote is a line that your graph gets closer and closer to but never touches or crosses it.
ohhh, so for the blue line it's on the x=-50, btw do you know the scale for this graph?
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
do you know how I can graph this onto my graphing calculator (TI-83+)? Because I didn't get the same graph o.o
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
not sure how to set the viewing rectangle on your TI83
why x -20 to -70 and y from -7 to 7?
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
ohh, but say this was on the test how would you know what to set?
trial and error more or less.
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
ooh. Really?? How does it tell me?
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.
example: f(x)=2x+1 shift 3 units left: f(x)=2(x-3)+1
ooops...shift 3 units left is f(x)=2(x+3)+1 watch your signs!
ohh, i see. But how do I read C(x) = 20/(50+x)?
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)
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: