A function is defined by $f(x)=\dfrac{5x-2}{2x-3}$, where $x\ne \frac{3}{2}$. Write down th

Question

A function is defined by $f(x)=\dfrac{5x-2}{2x-3}$, where $x\ne \frac{3}{2}$. 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

(a) $x=\frac32$, $y=\frac52$. (b) $x$-intercept $\left(\frac25,0\right)$; $y$-intercept $\left(0,\frac23\right)$. (d) For $y=f(|x|)$, the vertical asymptotes are $x=\pm\frac32$, the horizontal asymptote is $y=\frac52$, and the axial intercepts are $\left(\pm\frac25,0\right)$ and $\left(0,\frac23\right)$.

Graphing Techniques - Sketching Rational Functions

Graphing Techniques - Sketching Rational Functions

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