QUESTION 4 It is given that the asymptotes of $$ f(x)=\frac{6}{x+p}+q $$ intersect at $$ (4 ; 3) $$. $$ 4.1 \quad $$ Write down the equation of $$ f $$. $$ 4.2 \quad \begin{array}{l} ext { Sketch the graph of } f ext {, clearly showing all the intercepts with the axes and any } \ ext { asymptotes. }\end{array} $$ $$ 4.4 \quad \begin{array}{l}g ext { is one of the axes of symmetry of } f ext { and it is a decreasing function. Determine the } \ ext { equation of } g ext {. } \ 4.5 \ (-3 ; 2) ext { is a point on } f ext {. Determine the coordinates of the image of this point after } \ ext { reflection in } g ext {. }\end{array} $$

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QUESTION 4 It is given that the asymptotes of $$ f(x)=\frac{6}{x+p}+q $$ intersect at $$ (4 ; 3) $$. $$ 4.1 \quad $$ Write down the equation of $$ f $$. $$ 4.2 \quad \begin{array}{l}	ext { Sketch the graph of } f 	ext {, clearly showing all the intercepts with the axes and any } \ 	ext { asymptotes. }\end{array} $$ $$ 4.4 \quad \begin{array}{l}g 	ext { is one of the axes of symmetry of } f 	ext { and it is a decreasing function. Determine the } \ 	ext { equation of } g 	ext {. } \ 4.5 \ (-3 ; 2) 	ext { is a point on } f 	ext {. Determine the coordinates of the image of this point after } \ 	ext { reflection in } g 	ext {. }\end{array} $$

Joseph Long · Accepted Answer

**Simplified Answers:** 1. **4.1. Equation of $$ f $$:** $$ f(x) = \frac{6}{x - 4} + 3 $$ 2. **4.2. Graph of $$ f $$:** - **Vertical Asymptote:** $$ x = 4 $$ - **Horizontal Asymptote:** $$ y = 3 $$ - **X-intercept:** $$ (2, 0) $$ - **Y-intercept:** $$ (0, 1.5) $$ 3. **4.4. Equation of $$ g $$:** $$ g: \quad y = -x + 7 $$ 4. **4.5. Coordinates After Reflection:** $$ (5, 10) $$

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