finite Geometric Sequences ercise 4: (answers on page 341 ) Determine the sum of each of the following infinite geometric sequences below: \( \begin{array}{ll}\text { a) } 5+\frac{5}{2}+\frac{5}{4}+\ldots & \text { c) } 20+2+0,2+\ldots \\ \text { b) } 6 x-2 x+\frac{2 x}{3}-\ldots & \text { d) } \sum_{x=1}^{\infty} 2^{1-x}\end{array} \)

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: \( 3.1 \quad \) 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 \( g(x)=-2 \cdot 2^{x-1}+1 \)

a) Sketch the curve with equation where \( a \) is a constant and \( a>1 \) On your sketch show - the coordinates of the point of intersection of the curve with the \( y \)-axis - the equation of the asymptote to the curve.

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).

a) Sketch the curve with equation \[ y=a^{-x}+4 \] where \( a \) is a constant and \( a>1 \) On your sketch show

Sketch the curve with equation \[ y=a^{-x}+4 \]