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Asymptotes occur in places where the equation is not valid E.g the equation (1-2x)/x is not valid when x=0 (otherwise you'd be dividing by zero, which is not allowed). Thus there is a asymptote along the x-axis.
If you have an equation in a similar form to the one above (i.e a/b) , look at the denominator (b) and work out where it is not valid. This is generally the easiest method of finding asymptotes.
Other ways include "trial and error" - subbing in numbers and finding the place where it becomes mathematically impossible to have the equation running along that point.
Sometimes it is easier to sub a few numbers into the equation to begin with, and draw a sketch of where you think it goes. This should highlight areas /how many asymptotes to expect; after that you just have to find out exact locations.
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How do you find horizontal and vertical asymptotes?
finding vertical asymptotes is easy. lets use the equation y = (2x-2)/((x^2)-2x-3) since its a rational equation, all we have to do to find the vertical asymptotes is find the values at which the denominator would be equal to 0. since this makes it an undefined equation, that is where the asymptotes are. for this equation, -1 and 3 are the answers for the vertical ayspmtotes. the horizontal asymptotes are a lot more tricky. to solve them, simplify the equation if it is in factored form, then divide all terms both in the numerator and denominator with the term with the highest degree. so the horizontal asymptote of this equation is 0.
Place the steps to sketch the graph of a rational function in the appropriate order?
answer is:Find the function's zeros and vertical asymptotes, and plot them on a number line.Choose test numbers to the left and right of each of these places, and find the value of the function at each test number.Use test numbers to find where the function is positive and where it is negative.Sketch the function's graph, plotting additional points as guides as needed.
How do you find the equation of a graph?
You find the equation of a graph by finding an equation with a graph.
Why do inversely proportional functions have asymptotes?
Because the two variables cannot be zero voltage = current*resistance if we draw graph current against resistance we would see a exponential graph which means the two variables are inversely proportional but either cannot be zero because voltage is not equal to 0 n.j.p
The vertical of the function cosecant are determined by the points that are not in the domain?
The answer depends on what you mean by "vertical of the function cosecant". cosec(90) = 1/sin(90) = 1/1 = 1, which is on the graph.
