• $f(\vert x\vert)$: Horizontal reflection of the graph of $f$ for $x\ge0$.
• $\vert f(x)\vert$: Vertical reflection of the negative part of the graph of $f$.
• $1/f(x)$: roots of $f$ (solutions of $f(x)=0$) are transformed into vertical asymptotes; monotonicity is transformed into inverse monotonicity (if $f$ is increasing, $1/f$ is decreasing); when $\vert f(x)\vert = 1$, graphs $f$ and $1/f$ intersect.
• $y^2=f(x)$: when $f(x)\lt 0$, $y$ is undefined; if $f(x)\ge 0$, $y$ is the graph superposition of the graphs of the functions $\sqrt{f(x)}$ and $-\sqrt{f(x)}$; monotonicity of $\sqrt{f(x)}$ and $f$ is same; when $f(x) = 1$, graphs $f$ and $\sqrt{f}$ intersect.
$\sin x$. A: $f(\vert x\vert)$; B: $\vert f(x)\vert$; C: $1/f(x)$; D: $y^2=f(x)$" src="https://www.toktol.com//Content/images/transparent.gif" onload="conditionalLoadImage(this, 'https://toktolweb.blob.core.windows.net/courseimages/', 'dfunction_18.png', true, { width: 191, height: 160 }, 'https://toktolwebcdn.blob.core.windows.net/quizimages/')" name="dfunction_18.png" sub="Transformation of graph of $\sin x$. A: $f(\vert x\vert)$; B: $\vert f(x)\vert$; C: $1/f(x)$; D: $y^2=f(x)$" />
Transformation of graph of $\sin x$. A: $f(\vert x\vert)$; B: $\vert f(x)\vert$; C: $1/f(x)$; D: $y^2=f(x)$