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 \( f \) 3.1 Shift two units to the left 3.2 Shift 3 units up Shift 1 unit right and 2 units down 3.4 The equation of the new hyperbola has new asymptotes at \( x \) QUESTION 4 Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and Clearly indicate all intercepts with the axes, turning point(s) and asymp

It seems that I am unable to plot the graphs directly. However, I can guide you on how to sketch the graphs based on the information we have gathered. ### Steps to Sketch the Graphs 1. **Graph of the Hyperbola \( f(x) = \frac{3}{x - 7} - 4 \)**: - **Asymptotes**: Draw a vertical line at \( x = 7 \) and a horizontal line at \( y = -4 \). - **Behavior**: The hyperbola will approach these asymptotes but never touch them. It will have two branches: - One branch will be in the first quadrant (above the horizontal asymptote and to the right of the vertical asymptote). - The other branch will be in the third quadrant (below the horizontal asymptote and to the left of the vertical asymptote). 2. **Graph of the Parabola \( g(x) = -2x^2 - 4x + 6 \)**: - **Intercepts**: Plot the points \( (0, 6) \), \( (-3, 0) \), and \( (1, 0) \). - **Turning Point**: Mark the turning point at \( (1, 0) \). - **Shape**: Since the parabola opens downwards (as \( a = -2 < 0 \)), draw a downward-facing curve that passes through the intercepts and the turning point. ### Final Notes - Ensure to label the axes and the intercepts clearly. - The hyperbola and the parabola will not intersect since they are different types of functions. If you have graphing software or a graphing calculator, you can input the functions to visualize them accurately. If you need further assistance or have any other questions, feel free to ask!