Question

17. Reprezinta in acelasi sistem de axe ortogonale reprezentarile geometrice ale graficlor celor doua functii si apoi determina, daca este cazul, coordonatele punctului de intersectie a reprezentarilor geometrice a graficelor celor doua functii
a)f,g :R->R, f(x)=-x+1 si g(x)=x-3
b)f,g: R->R, f(x)=4x+1 si g(x)=4x-3
c)f,g:R->R,f(x)=2x+1 si g(x)=3x+2
d) f,g :R->R, f (x)=-2x-1 si g(x)=-3x+2
e)f,g:R->R,f(x)=2x+1 si g(x)= -2x-3
AM NEVOIE URGENTA!!!DAU SI COROANA!!

Answer 1

a.

f(x)=-x+1

g(x)=x-3

Coordonatele punctului de intersectie:

f(x)=g(x)

-x+1=x-3

2x=4

x=2

f(2)=-2+1=-1

M(2,-1)

Gf ∩OX, y=0

-x+1=0

x=1 A(1,0)

Gf ∩OY, x=0⇒ y=0+1=1 B(0,1)

Gg OX, y=0

x-3=0

x=3 C(3,0)

Gg ∩OY, x=0 ⇒ y=0-3=-3 D(0,-3)

b.

f(x)=4x+1

g(x)=4x-3

Coordonatele punctului de intersectie:

f(x)=g(x)

4x+1=4x-3

1=-3 Fals⇒ nu se intersecteaza

Gf ∩OX, y=0

4x+1=0

$x=-\frac{1}{4} \\\\A(-\frac{1}{4} ,0)$

Gf ∩OY, x=0⇒ y=0+1=1 B(0,1)

Gg ∩OX, y=0

4x-3=0

$x=\frac{3}{4} \\\\C(\frac{3}{4},0)$

Gg ∩OY, x=0⇒ y=0-3=-3 D(0,-3)

c.

f(x)=2x+1

g(x)=3x+2

Coordonatele punctului de intersectie:

f(x)=g(x)

2x+1=3x+2

x=-1

f(-1)=-2+1=-1

N(-1,-1)

Gf∩OX, y=0

2x+1=0

$x=-\frac{1}{2} \\\\A(-\frac{1}{2} ,0)$

Gf∩OY,x=0⇒ y=0+1=1 B(0,1)

Gg∩OX, y=0

3x+2=0

$x=-\frac{2}{3} \\\\C(-\frac{2}{3} ,0)$

Gg∩OY, x=0⇒ y=0+2=2 D(0,2)

d.

f(x)=-2x-1

g(x)=-3x+2

Coordonatele punctului de intersectie:

f(x)=g(x)

-2x-1=-3x+2

x=3

f(3)=-7

P(3,-7)

Gf∩OX, y=0

-2x-1=0

$x=-\frac{1}{2} \\\\A(-\frac{1}{2} ,0)$

Gf∩OY, x=0⇒ y=0-1=-1 B(0,-1)

Gg∩OX, y=0

-3x+2=0

$x=\frac{2}{3} \\\\C(\frac{2}{3} ,0)$

Gg∩OY, x=0⇒ y=0+2=2 D(0,2)

e.

f(x)=2x+1

g(x)=-2x-3

Coordonatele punctului de intersectie:

f(x)=g(x)

2x+1=-2x-3

4x=-4

x=-1

f(-1)=-2+1=-1

R(-1,-1)

Gf∩OX, y=0

2x+1=0

$x=-\frac{1}{2} \\\\A(-\frac{1}{2} ,0)$

Gf∩OY,x=0⇒ y=0+1=1 B(0,1)

Gg∩OX,y=0

-2x-3=0

$x=-\frac{3}{2} \\\\C(-\frac{3}{2} ,0)$

Gg∩OY, x=0⇒ y=0-3=-3 D(0,-3)