1. Algebra and Calculus 2-1 Copyright © Genetic Computer School 2007 Lesson 2 Graphs and Estimation (Part I)

2. Algebra and Calculus 2-2 Copyright © Genetic Computer School 2007 Lesson 2 Overview What is a graph? Tables of values Plotting the graph Polynomials Sketching curves

3. Algebra and Calculus 2-3 Copyright © Genetic Computer School 2007 What is a graph? Graph is a visual method of showing the behaviour of a function On occasion, a graph may be the only way to describe a function (a sensor may monitor a patient's heartbeat - the trace on a screen is a graph, but no one could find an equation to give the heartbeat at any particular instant)

4. Algebra and Calculus 2-4 Copyright © Genetic Computer School 2007 Tables of values To plot a graph  Need a set of points  Need a range of values of x and y E.g. y = 3x+1 X123 y4710

5. Algebra and Calculus 2-5 Copyright © Genetic Computer School 2007 Plotting the graph From Tables of values, we can easily draw points with co-ordinates (x i,y i ) on the axes. x y xixi yiyi

6. Algebra and Calculus 2-6 Copyright © Genetic Computer School 2007 Polynomials A function f(x) is a polynomial expression if it can be written in the form f(x)=a+bx+cx 2 +dx 3 +ex 4 +.... where a, b, c, d, e etc are all constant

7. Algebra and Calculus 2-7 Copyright © Genetic Computer School 2007 Sketching curves Linear curves Where it crosses the x-axis (when f(x) = 0) Where it crosses the y-axis (when x = 0) That it is a straight line

8. Algebra and Calculus 2-8 Copyright © Genetic Computer School 2007 Sketching curves Quadratic curves Where it crosses the y-axis (when x = 0) The general shape, form the sign of the coefficient of x 2 Where it crosses the x-axis, by solving the equation f(x) = 0 The maximum/minimum point when 2ax + b = 0, that is at x = -b/2a and f(-b/2a)

9. Algebra and Calculus 2-9 Copyright © Genetic Computer School 2007 Sketching curves Cubic curves ax 3 + bx 2 + cx + d Find where it crosses the y-axis (when x = 0)

10. Algebra and Calculus 2-10 Copyright © Genetic Computer School 2007 Exponential curves The curve must go through (0,1) The whole graph is bound to be above the x-axis