Let g(z) = z-i z+i' (a) Evaluate g(i) and g(1). (b) Evaluate the limits lim g(z), and lim g(z). 2-12 (c) Find the image of the real axis under g. (d) Find the image of the upper half plane {z: Iz > 0} under the function g.
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- 8x-7 4. Let f)7x + 10 (a) Find f (x). (b) Find thedomain of/. (c) Find the domain of f (d) Find the range ofa) Draw y = f(x)] b) Draw y = [f(x)]² 1+ (1, -1) (1, -1) 2 2 (2.5,1) (2.5,1) i) Explain two things that happen to the priginal graph for x < 0 and -1 < y < 0 ii) Explain what happens to the points on y = f(x) where y = 0 and y = 1 when you need to sketch y = [f(x)]². iii) For what values of x will [f(x)]²determine the horizontal asymtope of f(x) = 2X divided X -3A small aircraft starts its descent from an altitude of h =- miles, 4 milles west of the runway (see figure). (a) Find the cublc function f(x) = ax3 + bx2 + cx + d on the Interval [-4, 0] that describes a smooth glide path for the landing. f(x) = (b) The function in part (a) models the glide path of the plane. When would the plane be descending at the greatest rate? X =Sketch and find the domainUsing the function f: (-1,2] → R, ƒ (x) = 4x³ – 3x² – 6x + 2, a. Determine all the stationary points within the domain restriction and the nature of each of these turning points b.-Sketch the graph of the function in the space below, indicating the endpoints, y- intercepts, and the turning points. Show calculations for the start and end point in the space below too. ORMITUniversity Page 4 of 7 MM Quiz (2021)Find the funchion f Such that F(x) xf (x)-x and fo) 2Let f(x) = x2 + 3x- 2 f(x) – f(1) X - 1 a) Find lim x+1 b) Use your answer in part (a) to find an equation of the tangent line to the curve y = x +3x - 2 at the point (1,2).Consider the function f(x) = 4x - x² and the point P(1, 3) on the graph of f. (a) Graph fand the secant lines passing through P(1, 3) and Q(x, f(x)) for x-values of 2, 1.5, 0.5. Find the slope of each secant line. line passing through Q(2, f(x)) line passing through Q(1.5, f(x)) line passing through Q(0.5, f(x)) (b) Use the results of part (a) to estimate the slope of the tangent line to the graph of fat P(1, 3). MY NOTES Describe how to improve your approximation of the slope. Define the secant lines with points farther away from P. Choose secant lines that are nearly horizontal. O Define the secant lines with points closer to P. Choose secant lines that are nearly vertical. ASK YOUR TEACHERSketch the graph of f (x) = x2 + 1 over the interval [-2,2]Consider the two functionsf(x) = x^2 + 3x and g(x) = {x^2 − 2, x ≤ 0}, {x + 2, x > 0}(a) Evaluate(i) (f + g)(−2)(ii) (fg)(1)(iii) (f /g)(2)(b) Using algebra, find all the points (x and y coordinates) where the graphs of f(x) and g(x) intersect, showing all working