two important features are the asymptotes and the holes of the graph. Use algebraic techniques to determine the vertical asymptotes and holes of any rational equation so that you can
To find a vertical asymptote, first write the function you wish to determine the asymptote of. Most likely, this function will be a rational function, where the variable x is included somewhere in the denominator. As a rule, when the denominator of a rational function approaches zero, it has...
Step 5:Determine the range by looking at the graph from bottom to top, writing anyy-values included in the graph in interval notation. Vocabulary for Finding the Intercepts, Asymptotes, Domain, and Range From the Graph of a Rational Function ...
Determine the horizontal asymptote of the following: f(x) = \dfrac{2x^2}{x^2 + 3x -4}. Find the vertical asymptote for the function f(x) = x-1/x^2-x. Why does an exponential function not cross the horizontal asymptote? How do you find the horizontal asymptotes of a logarithmic...
And if your interval length is infinity, there’s no way to determine that interval. The workaround is to turn the improper integral into a proper one and then integrate by turning the integral into a limit problem. Limits for improper integrals do not always exist; An improper integral is...
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If the ratio 1 is equal to b/a then 1 = 1/a a = 1/1 a = 1 Determine hypotenuse if the adjacent side (b) is 1 and the opposite side (a) is 1? You can calculate the hypotenuse using Pythagoras theorem which states that the squared hypotenuse is equal to the sum of the squared...
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Plug the value x = 0 into the rational function and determine the value of f(x) to find the y-intercept of the function. For example, plug x = 0 into the rational function f(x) = (x^2 – 3x + 2) / (x – 1) to get the value (0 – 0 + 2) / (0 – 1), which is...
Step 3:For each factor in the denominator, check for the same factor in the numerator and determine the type of discontinuity. If no same factors exist, then at this value ofxthat makesf(x)undefined, there is a vertical asymptote.