Section 1.4 Graphing Calculators and Computers

Section 1.4Graphing Calculators and Computers AP Calculus September 8, 2008 CASA

Calculators: A Cautionary Tale • Calculators help us do things that are difficult to do by hand, but as helpful as they are, calculators are not a substitute for thinking • While taking the AP exam, you are expected to do many things without the calculator. • While taking the AP exam, there are some tasks that require the use of a calculator. • Your job: Know the advantage and disadvantages. Calculus, Section 1.4

f(x) = sin(50x) as viewed in [-12,12] by [-1.5,1.5] Calculus, Section 1.4

What’s going on here? • Calculators, like all computers, following instructions. Groups of instructions are called programs. • The graphing program in the TI-83 finds values of x based on pixel location. This is not the best way to graph sometimes. Calculus, Section 1.4

So what are we to do? • Think • Use your knowledge of mathematics • Think • Adjust as necessary • Think Calculus, Section 1.4

Think about what? • Think about the last example • What do we know about how sine is transformed when x is replaced by 50x? • The period is reduced to pi/25. Calculus, Section 1.4

Think about what? • If the period is reduced to pi/25, then what is the best viewing window? • [-pi/25,pi/25] by [-1.5,1.5] Calculus, Section 1.4

Plan of attack: Trig. functions • Adjust to the period • Adjust to the amplitude • Adjust to vertical transformation Calculus, Section 1.4

Plan of attack: Trig. functions • Adjust to the period: pi • Adjust to the amplitude: 30*2 • Adjust to vertical transformation: up 50 • [-pi/2,pi/2] by [15,85] Calculus, Section 1.4

Plan of attack: Polynomials • What happens at the extremes? • What is the maximum number of zeros? • Where are the zeros? • Capture all the zeros, all local maxima and all local minima. Calculus, Section 1.4

Plan of attack: Polynomials • [-10,10] by [-10,200] • Note: I also adjust the Xscl and Yscl. This places tick mark on the axes, making the graph easier to read. • Xscl = 1 • Yscl = 25 Calculus, Section 1.4

Plan of attack: Rationals • What happens at the extremes? • What is the maximum number of zeros? • Where are the zeros? • Are there any vertical asymptotes? • Capture the all zeros, all local maxima and all local minima. • Start with ZStandard Calculus, Section 1.4

Plan of attack: Rationals • What happens at the extremes? • What is the maximum number of zeros? • Where are the zeros? • Are there any vertical asymptotes? • Capture the all zeros, all local maxima and all local minima. Calculus, Section 1.4

Plan of attack: Rationals • What happens at the extremes? • What is the maximum number of zeros? • Where are the zeros? • Are there any vertical asymptotes? • Capture the all zeros, all local maxima and all local minima. • [-10,10] by [-25,25] • Yscl: 5 Calculus, Section 1.4

Assignment • Section 1.4, 1-41 odd for next class • We will be prepared for your first test during the next class. The in-class assignment will be… • Chapter 1 Review, Exercises: 1-21, all Calculus, Section 1.4

Section 1.4 Graphing Calculators and Computers