Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s).

3-Determine the domain of \( f(x, y)=\sqrt{x^{2}-9}-\ln (y-1) \) \[ \begin{array}{ll}\text { (a) }|x| \geq 3 \text { and } y>1 & \text { (b) }|x| \leq 3 \\ \text { (c) }|x| \geq 3 \text { and } y=1 & \end{array} \]

Identify the trace of the surface \( 3 x+2 x^{2}-z^{2}-2 y=5 \) on \( y z \)-plase \( \begin{array}{llll}\text { A. Ellipse } & \text { (B) Circle } & \text { C. Hyperbola } & \text { D. Par }\end{array} \)

What effect does multiplying the function \( f(x) = 3^x \) by -1 have on its graph? Describe any transformations.

3) Soit \( \left(v_{n}\right) \) la suite numérique définie par \( v_{n}=\frac{2-u_{n}}{1-u_{n}} \), pour tout entier naturel \( n \) a) Montrer que \( \left(v_{n}\right) \) est une suite géométrique de raison \( \frac{2}{3} \) b) Montrer que \( u_{n}=1+\frac{1}{1-\left(\frac{2}{3}\right)^{n+1}} \), pour tout entier naturel \( n \)

18) \( \frac{1}{1+\log _{b} a+\log _{b} c}+\frac{1}{1+\log _{c} a+\log _{c} b}+\frac{1}{1+\log _{a} b+\log _{a} c}=\ldots \ldots \ldots \) \( \begin{array}{lll}\text { a) } \log _{a} b c & \text { b) } \log _{b} a c & \text { c) } \log ^{2}\end{array} \)