Question

In MATLAB:

(a) Insert a comment in your script that says Problem 1:

(b) Below this comment, generate a vector of values called x that starts at −10, ends at 8, and has a step size of 0.1 between points.

(c) Define the function f(x) = (x − 6)(x 2 − 1)(x + 8) in your script, then plot f(x) against x.

(d) Plot the x- and y-axes on the plot in part (c). Mark each of the x-intercepts on this plot (you will need the hold on command).

(e) Label the x- and y-axes (you will need the xlabel and ylabel commands).

Answer 1

% Problem 1:

% Matlab script to calculate and plot the function f(x) for given values of
% x and plot the x-intercepts points for this function
% define the vector x that starts from -10 and end at 8 with steps of 0.1
x = (-10:0.1:8);

%define the function
f = @(x) (x-6).*((x.^2)-1).*(x+8);

y = f(x); % calculate the value of f at x points

plot(x,y); % plot y vs x
hold on; % used to plot in the same graph

% find is used to return the indices corresponding to the entries
% satisfying the given condition
% Here it will return the indices of y vector where value of function is 0
I = find(y==0);

% plot x-axes and y-axes

xL = xlim; % get the x limits for the current axes
yL = ylim; % get the y limits for the current axes

line([0 0],yL); % plot y-axis
line(xL,[0 0]); % plot x-axis

%plot the x-intercepts with red circles
plot(x(I),y(I),'ro');
hold off; % release the current plot
xlabel('x'); % label the x-axes
ylabel('f(x)'); % label the y-axes
% set the title
title('Plot of f(x) v/s x marking each of x-intercepts');
%end of script

Output: