Question

AM NEVOIE URGENT PÂNĂ MÂINE LA 9, EX 7,8,9. VA ROG, DAU COROANA!!​

Answer 1

7. f:[-4;3] -> R, f(x) = 2x + 1

A(-1; -1) ∈ Gf <=> f(-1) = -1 <=> -2 + 1 = -1 <=> -1 = -1 (A) => A ∈ Gf

B(-2; 3) ∈ Gf <=> f(-2) = 3 <=> -4 + 1 = 3 <=> -3 = 3 (F) => B ∉ Gf

C(1; 3) ∈ Gf <=> f(1) = 3 <=> 2 + 1 = 3 <=> 3 = 3 (A) => C ∈ Gf

D(2; 5) ∈ Gf <=> f(2) = 5 <=> 4 + 1 = 5 <=> 5 = 5 (A) => D ∈ Gf

E(0; 2) ∈ Gf <=> f(0) = 2 <=> 0 + 1 = 2 <=> 1 = 2 (F) => E ∉ Gf

Concluzie: Punctele A, C, D apartin graficului functiei.

8. f:(-3;2) -> R, f(x) = 3x + a

a) A(-2; -3) ∈ Gf <=> f(-2) = -3 <=> -6 + a = -3 => a = 3 ∈ R

b) f(x) = 3x + 3

Luam arbitrar doua puncte, sa zicem M(0, f(0)) = M(0, 3) si N(1, f(1)) = N(1, 6). Le reprezentam in sistemul de axe xOy si trasam o dreapta care sa uneasca cele doua puncte.

9. f:R -> R, f(x) = ax + 2

a) A(1; 3) ∈ Gf <=> f(1) = 3 <=> a + 2 = 3 => a = 1 ∈ R

b) f(x) = x + 2

Idem exercitiu 8, consideram M(0, f(0)) = M(0, 2) si N(1, f(1)) = N(1, 3).