The diagram shows the curve $y=\mathrm{f}\left( x \right)$. The curve has maximum points at \(\lef

Question

The diagram shows the curve $y=\mathrm{f}\left( x \right)$. The curve has maximum points at $\left( -5,4 \right)$ and the origin, and crosses the $x$-axis at $\left( -4,0 \right)$. The lines $y=0$, $x=-3$ and $y=-x+2$ are the horizontal, vertical and oblique asymptotes to the curve respectively. $y=\frac{1}{\mathrm{f}\left( x \right)}$[3] $y=\mathrm{f}\left( \frac{x+1}{2} \right)$[3] labelling clearly the equation(s) of any asymptote(s), coordinates of any axial intercept(s) and turning point(s) where applicable.

Accepted Answer

(a) Vertical asymptotes $x=-4$ and $x=0$, right-hand horizontal asymptote $y=0$, minimum $\left(-5,\dfrac14\right)$, hole at $(-3,0)$, no axial intercepts (b) Vertical asymptote $x=-7$, horizontal asymptote $y=0$, oblique asymptote $y=-\dfrac{x}{2}+\dfrac32$, maximum $(-11,4)$, curve intercepts $(-9,0)$ and $(-1,0)$

2017 RI P1 Q5

2017 RI P1 Q5

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