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1 - Amosam
1 - Amosam

... If g(x) = x3 + x2 and f(x) = 2x – 5, then h(x) = f(g(x)) = f(x3 + x2) = 2(x3 + x2) – 5 The range of g(x) becomes the domain of f(x). For example in the above function, if the domain for g(x) is 2, the range value becomes 12. This becomes the domain for f(x), producing a range value of 19. We can say ...
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... 1. Reduce R ( x ) to lowest terms. 2. Determine the x-intercepts by setting the numerator equal to zero. 3. Determine the y-intercepts by finding R ( 0 ) . 4. Determine the equation (x = ___ ) of all vertical asymptotes by setting the denominator equal to zero. Graphs will never cross the vertical a ...
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Asymptote



In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors. In some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity.The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means ""not falling together"", from ἀ priv. + σύν ""together"" + πτωτ-ός ""fallen"". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.There are potentially three kinds of asymptotes: horizontal, vertical and oblique asymptotes. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotes are vertical lines near which the function grows without bound.More generally, one curve is a curvilinear asymptote of another (as opposed to a linear asymptote) if the distance between the two curves tends to zero as they tend to infinity, although the term asymptote by itself is usually reserved for linear asymptotes.Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph. The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.
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