The graph of $y = \mathrm{f}(x)$ cuts the $x$-axis at the point $(6,0)$ and has a maximum poin

Question

The graph of $y = \mathrm{f}(x)$ cuts the $x$-axis at the point $(6,0)$ and has a maximum point and a minimum point at $(0,0)$ and $(3,-5)$ respectively. The graph of $y = \mathrm{g}(x)$ cuts the $x$-axis at the point $(2,0)$, and has a minimum point and a maximum point at $(0,0)$ and $(1,5)$ respectively. The diagrams below show the graphs of $y = \mathrm{f}(x)$ and $y = \mathrm{g}(x)$. Describe fully a sequence of two transformations which transforms the graph of $y = \mathrm{f}(x)$ onto the graph of $y = \mathrm{g}(x)$.[2] It is given that $\mathrm{g}(x)$ can be expressed in the form $a\mathrm{f}(bx+c)+d$ where $a$, $b$, $c$ and $d$ are constants. State the values of $a$, $b$, $c$ and $d$.[2] The derivative of the function $y = \mathrm{f}(x)$ with respect to $x$ is denoted by $\mathrm{f}'(x)$. It is given that $\mathrm{f}'(6) = 4$. Find the exact value of $\mathrm{g}'(2)$.[3]

Accepted Answer

(ii)a=-1, b=3 c=0, d=0 (iii)-12

2025 SAJC P1 Q6

2025 SAJC P1 Q6