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- 1) A y-intercept at the point 2) x-intercepts at the point(s) 3) Vertical asymptotes at x = 4) Horizontal asymptote at y =The equation of curve C is given to be ax² + bx +c_ Given that x = -1 is an y%3D %3D x +d asymptote, and the curve passes through the point (1,3) , (3,4) and (5,7). (a) Find the values of a, b, c and d. (b) Hence, sketch the graph, indicating the asymptotes and axial intercepts clearly.The asymptotes of (x²/a²) – (y²/b²) = 1 Show that the vertical distance between the line y = (b/a)x and the upper half %3D of the right-hand branch y = (b/a)Vx² – a² of the hyperbola (x²/a²) – (y³/b²) = 1 approaches 0 by showing that lim * -V - a) = lim (x – V - a) = 0. x→00 Similar results hold for the remaining portions of the hyperbola and the lines y = ±(b/a)x.
- (3) Let R(x) = 2432-4 (b))Determine the asymptotic behavior of the graph of R(r) when z tends to the vertical asymptotes from the left and right. 05 154 6.Use a graph to estimate all the vertical and horizontal asymptotes of the curve y=7- 2x + 1 x' - 2x + 1You are given the following graph of the function f(x): 10 5.0 1.0 -10 Find the point where the second derivative changes sign from negative to positive? X=
- What does it mean to say that y = b is a horizontal asymptote of y = f(x) ?Sketch the graph and show all extrema, inflection points, and asymptotes where applicable. 1) f(x) = x1/3(x2 - 252) 400+ 200+ -10 10 20 X -200+ A) Rel max: (-6, 216 6), Rel min: (6, -216 6) Inflection point: (0,0) 400+ 200 -20 -10 10 20 X 200 400 B) Rel min: (0, 0) No inflection points 400+ 200+ -20 -10 10 20 X -2004x +2 Let f(z) - z2 - z - 6 X-value of any holes Vertical asymptotes at x = Horizontal asymptote at y = Oblique asymptote at y =