Topic: Graphs
Name: Maigue, Carvey Ehren R.
Class Number:
Student Number: 2010100352
Course/Section: Math16-1L/E01
Schedule: T 7:30-12:00
Instructions: Solve the following problems by writing all the commands used and writing the final
answers
Plot each of the given functions using 30 data points from -10 to 10.
Function: 𝑦 = 𝑥 4 − 8𝑥 2 + 1
Function: 𝑦 = 𝑥 3 + 3𝑥 2 − 10𝑥 − 24
Commands:
Commands:
x = -10:0.67:10;
x = -10:0.67:10;
plot(x,x^4-8*x^2+16,'-*')
plot(x,x^3+3*x^2-10*x-24,'-*')
Graph:
Graph:
Graph 1/(1 + e^rx) for −5 ≤ x ≤ 5 for various values of r on one plot. Values of r : 1, 2, and 3.
Function:
y = 1/(1 + e^(1*x))
y = 1/(1 + e^(2*x))
y = 1/(1 + e^(3*x))
Commands:
x = -5:0.3:5;
plot(x,1./(1+%e.^(1.*x)),'ro.',x,1./(1+%e.^(2.*x)),'cya+',x,1./(1+%e.^(3.*x)),'-mo')
Graph:
Use plot2d to draw a graph that shows the following limit. limx→a f(x) = L. 𝑓(𝑥) = 3 + |2𝑥 − 4|, 𝑎 = 2, 𝐿
= 3. Select a suitable range and a set of values of x.
Function:
Graph:
𝑓(𝑥) = 3 + |2𝑥 − 4| (x>2)
𝑓(𝑥) = 3 + |2𝑥 − 4| (x<2)
Commands:
x=1:0.1:3;
plot2d(x,3+abs(2*x-4));
Plot the polar graph of r for 0 ≤ t ≤ 2π. Include a title for your graph.
Function: 𝑟 = 1 + 2 cos 𝜃
Function: 𝑟^2 = 3^2 sin 2𝜃
Commands:
Commands:
theta = 0:0.1:2*%pi;
theta=0:0.1:2*%pi;
polarplot (theta,1+2.*cos(theta))
rho=sqrt((3^2)*sin(2*theta));
title ('polar plot of r = 1+2cos(theta)')
polarplot(theta,real(rho),2);
title ('polar plot of r^2 = 3^2sin(2*theta)')
Graph:
Graph: