\( f ( x ) = x + \frac { 1 } { x } \rightarrow f ( 1 ) , f ( - 1 ) , f ( 2 ) , f ( \frac { 1 } { 2 } ) \)

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: \( 3.1 \quad \) Shift two units to the left \( 3.2 \quad \) Shift 3 units up Shift 1 unit right and 2 units down QU.3 The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \) Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \)

11. For \( b>0 \), what are the domain and range of \( f(x)=b^{x} \) ? Choose the correct domain below. (A. \( D=(0, \infty) \) B. \( D=[0, \infty) \) C. \( D=(-\infty, 0] \) D. \( D=(-\infty, \infty) \) Choose the correct range below. A. \( R=\{y: y<0\} \) B. \( R=\{y: y \leq 0\} \) C. \( R=\{y: y>0\} \) D. \( R=\{y: y \geq 0\} \)

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: \( \begin{array}{ll}3.1 \quad \text { Shift two units to the left } \\ 3.2 \quad \text { Shift } 3 \text { units up } \\ 3.3 \quad \text { Shift } 1 \text { unit right and } 2 \text { units down }\end{array} \)

- Parametrik tenglamalar bilan berilgan \( x=\sin 2 t, \quad y=\cos 2 t, \quad-\pi / 2<t<\pi / 2 \) egri chiziq Dekart koordinatalar sistemasidagi tenglamasini yozing.

If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real.