4722.sagews

x = var('x'); f1 = 7-3*x

puntos1=[(0,f1(0)), (1,f1(1)), (2,f1(2)), (3,f1(3)), (4,f1(4))]

g1=Graphics()

g1+=point(puntos1,size=20)

show(g1)

plot(f1,0,4)

#    EXAMPLE 1 Sketching a Graph by Point Plotting

f2=x^2-2; puntos2=[(-2,f2(-2)), (-1,f2(-1)), (0,f2(0)), (1,f2(1)), (2,f2(2)), (3,f2(3))]

g2=Graphics()

g2+=point(puntos2,size=20)

show(g2)

plot(f2,-2,2)

f3=x*(39-10*x^2+x^4)/30

puntos3=[(-3,f3(-3)), (-1,f3(-1)), (0,f3(0)), (1,f3(1)), (3,f3(3))]

g3=Graphics(); g3+=point(puntos3,size=20); show(g3)

plot(f3,-4,4))

f4=x^3-x^2-25; plot(f4,(x,-10,10),aspect_ratio=0.3)

plot(f4,-10,10)

#EXPLORATION

fa=x^3-3*x^2+2*x+5;plot(fa,-8,8)

fb=x^3-3*x^2+2*x+25;plot(fb,-8,8)

fc=-x^3-3*x^2+2*x+5;plot(fc,-8,8)

fd=3*x^3-40*x^2+50*x-45; plot(fd,-15,20)

fe=-(x+12)^3; plot(fe,-60,50)

ff=(x-2)*(x-4)*(x-6); plot(ff,0,8)

#    Intercepts of a Graph

f=(x^3-4*x); f.factor()

(x - 2)*(x + 2)*x

eqn=(f==0); solve(eqn,x)

[x == -2, x == 2, x == 0]

plot(f,-3,3)

f1=2*x^3-x; f2=-2*x^3+x

plot(f1)

plot(f2)

f3=sqrt(x-1); f4=-sqrt(x-1)

plot(f3,1,9)

plot(f4,1,9)

plot(f3,1,9)+plot(f4,1,9)

#    Points of Intersection

f=x^2-3; g=x-1; puntos=[(2,f(2)),(-1,f(-1))]

S=solve(f==g,x); show(S)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = 2, x = \left(-1\right)\right]

plot(g,-2.5,2.5)+plot(f,-2.5,2.5)+point(puntos,size=30,color='black')

#    EXAMPLE 6 Comparing Two Mathematical Models

t=var('t'); y1=316.2+0.70*t+0.018*t^2; y2=304.1+1.64*t

plot(y1,4,55)+plot(y2,(t,4,55),color='red')

y1(75);y2(75)

469.950000000000 427.100000000000

#    Exercises

y1=-3*x/2+3; y2=sqrt(9-x^2); y3=3-x^2; y4=x^3-x

#1
plot(y1,-1,3)

#2
plot(y2,(x,-3,3),aspect_ratio=1)

#3
t=text(r"$y_1=-\frac{3x}{2}+3$",(2,2),fontsize=14,rgbcolor=(0,0,0));
plot(y3,-3,3)+t

#4
plot(y4,-2,2)

f5=x/2+2; f6=5-2*x; f7=4-x^2; f8=(x-3)^2; f9=abs(x+2); f10=abs(x)-1; f11=sqrt(x)-6; f12=sqrt(x+2); f13=3/x; f14=1/(x+2)

plot(f5,-5,5)

plot(f6,-2,5)

plot(f7,-2,2)

plot(f8,-10,16)

plot(f9,-14,10)