To graph a rational function:Factor the numerator and denominator, if possible; check if anything can be cancelled out. Solve the numerator's factors for their zeroes; these will be the x-intercepts of the graph. Solve the denominator's factors for their zeroes, keeping in mind that the ...
For example, f(x) = 1/(3x+1) can be a rational function. But note that the denominators of rational functions cannot be constants. For example, f(x) = (2x + 3) / 4 is NOT a rational function, rather, it is a linear function....
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The x-intercepts lead to the conclusion that the numerator of the rational function must have the factors (x+3) and (x-1). The fact that there is a vertical asymptote at x=-2 means there must be at least one factor of (x + 2) in the denominator. In order to have a horizontal...
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I have a Rational function y = 1 / x^2-1 . I have a good idea what the graph looks it, it will have vertical asymptotes at -1 and 1 and I can work out the y intercept (-1 concave down). However I'm not sure about the other parts to the question. Homework Statement dy/dx...
x-intercept (so y = 0) 0=x+2x2+10=x+2−2=x00−2=x2+1x+2=x+2=xSo the intercepts are at (0, 2) and (−2, 0). I'll draw these points on the graph:Content Continues BelowI'm not sure, just from the one asymptote and the two points I have so far, quite what ...
Find the x-intercept(s), if any. Plug in 0 for y. Solve for x (only take real solutions). ( )In other words, find the real zeros of f x = x2 − 6x + 5 . 0 = x2 − 6x + 5 0 = (x − 5)(x − 1) x = 5 or x = 1 The x-intercepts are 1 and 5. ( ...
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mialfunction. (e)Solveapolynomialinequality. (f)Givetheequationsoftheverticalandhorizontalasymptotesof arationalfunctionfromeithertheequationorthegraphofthe function. (g)Grapharationalfunctionfromitsequation,withoutusinga calculator. (h)Givetheendbehaviorofarationalfunctionfromitsgraph,using “asx→a,f(x)...