Preparing for University Calculus - Math and Computer Science

3.9 GraphsYou should be able to graph polynomials and rational functions, showing featuressuch as zeroes, y intercept, horizontal, vertical, and slant asymptotes, and points ofdiscontinuity. You should also be able to read significant features from a graph.A graph - for our purposes - should be drawn by determining the main featuresand joining them together with smooth curves. It should not be drawn by plottingfive or six points and joining them with straight lines! In your calculus course, youwill learn to extend these graphing skills by adding other features, such as maxima,minima, and points of inflection.Examples:1. Which equation best fits the given curve?10-1 -1 1(a) y = x 2(b) y =1/x(c) y = sin(x)(d) x = −1/y(e) x = y 2Solution: As the graph has a vertical asymptote (here, x = 0), we can ruleout (a),(c), and (e). Of the remaining two options, (b) has a graph consistingof points in the first and third quadrants (x and y are either both positive orboth negative), while the equation (d) is satisfied by points such as (1, −1)that are on the given curve. So we choose (d), which does indeed have all theright features.2. Which of the following is the graph of a function y = f(x)?A10-1 -1 1B10-1 -1 1C10-1 -1 1(a) A only(b) B only(c) C only(d) all three(e) A and B(f) A and C26