The diagram shows the graphs of $y = \mathrm{f}(|x|)$ and $y = \mathrm{f}'(x)$. The graph of \(y

Question

The diagram shows the graphs of $y = \mathrm{f}(|x|)$ and $y = \mathrm{f}'(x)$. The graph of $y = \mathrm{f}(|x|)$ has turning points at $(-3, 4)$ and $(3, 4)$, crosses the $x$-axis at $(-2, 0)$ and $(2, 0)$, and the equations of asymptotes are $x = -1$, $x = 1$ and $y = 2$. The graph of $y = \mathrm{f}'(x)$ crosses the $x$-axis at $(3, 0)$, and the equations of asymptotes are $x = 1$ and $y = 0$. On separate diagrams, sketch the graphs of $y = \mathrm{f}(x)$,[2] $y = \frac{1}{\mathrm{f}'(x)}$,[3] $y = -\mathrm{f}(|x-1|)$,[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) Sketch shown: intercepts $(0,0),(2,0)$, maximum $(3,4)$, asymptotes $x=1$ and right-hand $y=2$. (b) Sketch shown: asymptote$x=3$, excluded hole $(1,0)$, no x-intercepts. (c) Sketch shown: asymptotes $x=0,2$,$y=-2$; zeros$-1,1,3$, minima$(-2,-4),(1,0),(4,-4)$, with a cusp at $(1,0)$.

2025 CJC P2 Q1

2025 CJC P2 Q1

Solution:

Solution locked