Si la fonction exponentielle a une forme \( f(x) = a^x + k \), comment détermineriez-vous les caractéristiques clés si \( k < 0 \) ?

10 The point of symmetry of the curve of the function \( f: f(x)=\frac{2 x+1}{x-1} \) is \( \begin{array}{llll}\text { (a) }(2,0) & \text { (b) }(2,1) & \text { (c) }(0,1) & \text { (d) }(1,2)\end{array} \)

QUESTION 3 The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows 3.1 Shift noo units to the left 3.2 Shif 3 units up 3.3 Shift 1 unit nght and 2 units down \( 3.4 \quad \) The equation of the new hypertola has new asymplotes at \( x-4 \) and \( y=-1 \)

I. \( 10 \frac{1}{\sqrt{m}+\sqrt{m+1}}=\sqrt{m+1}-\sqrt{m} \), determine, without the use of a calculator, the exact value of: \( \frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\ldots+\frac{1}{\sqrt{1680}+\sqrt{1681}} \)

Questão 11. (a) (Desigualdade de Bernoulli) Prove que \[ (1+x)^{n} \geq 1+n x, \quad \forall x \geq-1 \quad \text { e } \quad n \in \mathbb{N} . \] (Dica: Prove por indução sobre \( n \), ou seja: - mostre que a desigualdade é valida para \( n=1 \); - suponha que seja válida para \( n=k \), onde \( k \in \mathbb{N} \), então mostre que é válida para \( n=k+1 \).)

81 The range of the function \( f(x)=2-x^{2}, x \neq 0 \) is \( \ldots \ldots \ldots \ldots \ldots \) \( \begin{array}{llll}\text { (a) }]-\infty, 2] & \text { (b) }] 2, \infty[ & \text { (c) }] 0,2] & \text { (d) }[0,2]\end{array} \)