502 MrG What's an Exponential Function?

2541 days ago by MATH4R2013

#1) graph f(x)=2^(x) f(x)=2^(x) show(f) show(f(x)) show([f(x) for x in range(-2,3)]) show([f(x).n(digits=3) for x in range(-2,3)]) for x in range(-2,4): print(x,f(x)) f(x)=2^(x) plot([f(x)],xmin=-2,xmax=3) 
       




(-2, 1/4)
(-1, 1/2)
(0, 1)
(1, 2)
(2, 4)
(3, 8)
(-2, 1/4)
(-1, 1/2)
(0, 1)
(1, 2)
(2, 4)
(3, 8)
#2) graph f(x)=2^(-x) f(x)=2^(-x) show(f) show(f(x)) show([f(x) for x in range(-2,3)]) show([f(x).n(digits=3) for x in range(-2,3)]) for x in range(-2,4): print(x,f(x)) f(x)=2^(-x) plot([f(x)],xmin=-2,xmax=3) 
       




(-2, 4)
(-1, 2)
(0, 1)
(1, 1/2)
(2, 1/4)
(3, 1/8)
(-2, 4)
(-1, 2)
(0, 1)
(1, 1/2)
(2, 1/4)
(3, 1/8)
#3) graph f(x)=2^(-x)-3 and asymptote f(x)=2^(-x)-3 show(f) show(f(x)) show([f(x) for x in range(-2,3)]) show([f(x).n(digits=3) for x in range(-2,3)]) for x in range(-2,4): print(x,f(x)) f(x)=2^(-x)-3 plot([f(x),-3],xmin=-2,xmax=3) 
       




(-2, 1)
(-1, -1)
(0, -2)
(1, -5/2)
(2, -11/4)
(3, -23/8)
(-2, 1)
(-1, -1)
(0, -2)
(1, -5/2)
(2, -11/4)
(3, -23/8)
#4) solve for x: 3^(x+1)==81 show(solve(3^(x+1)==81,x)) r=solve(3^(x+1)==81,x) show(r) show(r[0]) show(r[0].rhs()) show(r[0].rhs().simplify_radical()) plot([3^(x+1),81],0,4) 
       





#5) solve for x: e^(-x^2)==e^(2*x)*e^(-3) show(solve(e^(-x^2)==e^(2*x)*e^(-3),x)) plot([e^(-x^2),e^(2*x)*e^(-3)],-4,2)