The curve $y=\mathrm{f}\left( x \right)$ has a horizontal asymptote $y=k$ and cuts the axes at $\lef

Question

The curve $y=\mathrm{f}\left( x \right)$ has a horizontal asymptote $y=k$ and cuts the axes at $\left( a,0 \right)$ and $\left( 0,b \right)$, where $a$, $b$ and $k$ are non-zero constants. It is given that ${{\mathrm{f}}^{-1}}\left( x \right)$ exists. State, if possible, the coordinates of the points where the following curves cut the axes and the equations of their asymptotes. $y=\mathrm{f}\left( 2x-3 \right)$ $y={{\mathrm{f}}^{-1}}\left( x \right)$ [2]

Accepted Answer

(i) y = k, x-int: ((a+3)/2, 0) (ii) x = k, intercepts: (0, a) and (b, 0)

2021 NYJC P1 Q5

2021 NYJC P1 Q5

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