# 함수와 그래프

## 2018 days 전, sky 작성

plot(1-x^2)
plot(x^3+1)
var('x, y') implicit_plot(x==y^2-1,(x,-2,2),(y,-2,2))
plot(2*x)
m=3 #93p 4번 b=2 f(x)=m*x+b plot(f(x), xmax=5, xmin=-5, ymax=5, ymin=-5)
m=-2 b=2 f(x)=m*x+b plot(f(x), xmax=5, xmin=-5, ymax=5, ymin=-5)
m=1/2 b=-3 f(x)=m*x+b plot(f(x), xmax=5, xmin=-5, ymax=5, ymin=-5)
m=-5 b=-1/4 f(x)=m*x+b plot(f(x))
m=-3/4 #93p 5번 b=5/4 f(x)=m*x+b plot(f(x), xmax=5, xmin=-5, ymax=5, ymin=-5)
m=2/5 b=6/5 f(x)=m*x+b plot(f(x), xmax=5, xmin=-5, ymax=5, ymin=-5)
plot(-2, color='purple')
f(y)=-1 plot(f(y), color='red')
m=0 b=-1 f(x)=m*x+b plot(f(x), xmax=5, xmin=-5, ymax=5, ymin=-5)
f(x)=3*x+4*y==5 #93P 5번 (Y절편 구하기) f(0)
 4*y == 5 4*y == 5
solve(x + sqrt( x + 5) == 7, x) #계산이 안됨 (104p 4(1))
 [x == -sqrt(x + 5) + 7] [x == -sqrt(x + 5) + 7]
solve((x-7)^2==(x+5), x) #식을 바꿔주니까 됨 (104p 4(1))
 [x == 4, x == 11] [x == 4, x == 11]
solve(x-sqrt(13-x)==1, x) #계산이 안됨 (104p 4(2))
 [x == sqrt(-x + 13) + 1] [x == sqrt(-x + 13) + 1]
solve(x-1==sqrt(13-x), x) #계산이 안됨 (104p 4(2))
 [x == sqrt(-x + 13) + 1] [x == sqrt(-x + 13) + 1]
solve((x-1)^2==(13-x), x) #식을 바꿔주니까 됨 (104p 4(2))
 [x == -3, x == 4] [x == -3, x == 4]
f(x)=x+sqrt(x+5) f(4)==7 #성립함(104p 4(1))
 7 == 7 7 == 7
f(x)=x+sqrt(x+5) f(11)==7 #성립하지 않음(104p 4(1))
 15 == 7 15 == 7
f(x)=x-sqrt(13-x) f(-3)==1 #성립하지 않음(104p 4(2))
 -7 == 1 -7 == 1
f(x)=x-sqrt(13-x) f(4)==1 #성립함(104p 4(2))
 1 == 1 1 == 1
solve(x^2 + abs(2*x-1) == 3, x) #105p3(1) 계산이 안됨
 [x == -sqrt(-abs(2*x - 1) + 3), x == sqrt(-abs(2*x - 1) + 3)] [x == -sqrt(-abs(2*x - 1) + 3), x == sqrt(-abs(2*x - 1) + 3)]
solve(x^2-3==-abs(2*x-1), x) #105p3(1) 계산이 안됨
 [x == -sqrt(-abs(2*x - 1) + 3), x == sqrt(-abs(2*x - 1) + 3)] [x == -sqrt(-abs(2*x - 1) + 3), x == sqrt(-abs(2*x - 1) + 3)]
solve(x^2+2*x-1==3, x) #105p3(1) _ 1 계산됨
 [x == -sqrt(5) - 1, x == sqrt(5) - 1] [x == -sqrt(5) - 1, x == sqrt(5) - 1]
solve(x^2-2*x+1==3, x) #105p3(1) _ 2 계산됨
 [x == -sqrt(3) + 1, x == sqrt(3) + 1] [x == -sqrt(3) + 1, x == sqrt(3) + 1]
solve(abs(x^2-1)==x+1, x) #105p3(2) 계산이 안됨
 [x == abs(x^2 - 1) - 1] [x == abs(x^2 - 1) - 1]
solve(x^2-1==x+1, x) #105p3(2) _ 1
 [x == 2, x == -1] [x == 2, x == -1]
solve(-x^2+1==x+1, x) #105p3(2) _ 2
 [x == -1, x == 0] [x == -1, x == 0]
f(x)=2*x-5*y==-6 f(0)/-5
 y == (6/5) y == (6/5)
solve(4*y == 5, y)
 [y == (5/4)] [y == (5/4)]
f(x)=2*x-5*y==-6 f(0)
 -5*y == -6 -5*y == -6
solve(-5*y == -6, y)
 [y == (6/5)] [y == (6/5)]
f(X)=y+1==0 f(0)
 y + 1 == 0 y + 1 == 0
solve(y+1 == 0, y)
 [y == -1] [y == -1]
implicit_plot(x==-6, (x, -10, 10), (y, -10, 10), axes=True)
implicit_plot(y==5, (x, -10, 10), (y, -10, 10), axes=True)