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Math help me please

I'm graphing a rational function. f(x) = (3x^2 + x - 4) / (2x^2 - 5x). The x-intercept is -4/3. The vertical asymptotes are x=0 and 5/2. Now my problem is I need to plot points between and beyond x-intercept and vertical asymptotes. What points do I choose from the graph. Hard to find out. Please help. Thank you.

Posted 154 day ago

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Answers (3)

atta
Given the vertical asymptotes x = 0, 5/2 && x-intercept(s) of -4/3, the points of this graph would be drawn between 0 and 2.5. Therefore, you would have a series of x-intercepts approaching the vertical asymptote (x = 0) from the left and a series of x-intercepts approaching the vertical asymptote (x = 2.5) from the right.

J.C

Posted 123 day ago

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samzappala
By graphing this formula, I set the horizontal to -1.33 and 2.75; verticle -60 and 18. The two verticle bars (asymptotes) are at 0,0 and 2.5,0. Choose pts ranging from .02,19 to .24,2.5 to 1.08, 0. to 1.5, -2.5 to 1.68, -2.5 to 2.3,-15 to 2.4,-44.2. The more, the better. These pts are between the asymptotes. These pts are from upper left to lower rt. Any pt on this graph intersecting the curve is what you're looking for.

Posted 153 day ago

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math_fanatic
You can find other points on the graph by choosing an x value that isn't 0, 5/2.

If the part of the function you're looking at lies between x= 0 and x = 5/2 then that means you can't choose an x value less than or equal to 0 or greater than or equal to 5/2. You also can't choose an x value that allows y to be -4/3.

So what are some numbers that lie between x=0 and x= 5/2?

There's 1/2, 1, 3/2, 2 to try. As long as these values don't yield a y value of -4/3, the coordinates will lie
on the curve of the function and meet the criteria stated in the problem.

I'll do x= 1 and x =2 for you since I don't have a calculator handy:
When x = 1, f(x) or y = 0
When x = 2, y = 10/-2 = -5

I don't think this is a continuous function though. There are clearly x values that lie outside the asymptotes for which this function would be defined. Perhaps you are only looking at a small section of it?



Posted 153 day ago

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