A function is defined by $f(x)=\dfrac{3x-2}{x+4}$, where $x\ne -4$. Write down the equation

Question

A function is defined by $f(x)=\dfrac{3x-2}{x+4}$, where $x\ne -4$. Write down the equations of the vertical and horizontal asymptotes of the graph of $y=f(x)$.[2] State the $x$- and $y$-intercepts of the graph of $y=f(x)$.[2] Sketch the graph of $y=f(x)$, clearly indicating the asymptotes and intercepts.[3] Hence, sketch the graph of $y=f(|x|)$ on a separate set of axes, clearly indicating any asymptotes and axial intercepts.[3]

Accepted Answer

$f(x)$: asymptotes $x=-4$, $y=3$; intercepts $\left(\frac23,0\right)$, $\left(0,-\frac12\right)$. $f(|x|)$: no vertical asymptote; horizontal asymptote $y=3$; intercepts $\left(\pm\frac23,0\right)$, $\left(0,-\frac12\right)$.

Transformations of a rational function and modulus

Transformations of a rational function and modulus

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