A function is defined by $f(x)=(x+1)(x-2)(x-5)$. Sketch the graphs of $y=f(x)$ and $y=f(-|x|)$

Question

A function is defined by $f(x)=(x+1)(x-2)(x-5)$. Sketch the graphs of $y=f(x)$ and $y=f(-|x|)$ on separate diagrams, clearly indicating their axial intercepts and any asymptotes.[8]

Accepted Answer

$y=f(x)$: intercepts $(-1,0)$, $(2,0)$, $(5,0)$, $(0,10)$. $y=f(-|x|)$: intercepts $(-1,0)$, $(1,0)$, $(0,10)$; symmetric about the $y$-axis. Neither graph has asymptotes.

Cubic graph transformation with negative modulus

Cubic graph transformation with negative modulus

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