# Tag Archives: Transformation # Reflections of Graphs

For $y=-f(x)$, we reflect $y=f(x)$ in the $x$-axis. For $y=f(-x)$, we reflect $y=f(x)$ in the $y$-axis. Example 1 Consider $f(x)=x^3-4x^2+4x$. On the same axes, sketch the graphs of $y=f(x)$ and $y=-f(x)$. \begin{align} \displaystyle f(x) &= x^3-4x^2+4x \\ &= x(x^2 – 4x + 4) \\ &= x(x-2)^2 \end{align} Example 2 Consider $f(x)=x^3-4x^2+4x$. On the […] # Must-Know 10 Basic Translations of Rational Functions Explained

Rational functions are characterised by the presence of both a horizontal asymptote and a vertical asymptote. Any graph of a rational function can be obtained from the reciprocal function $f(x)=\dfrac{1}{x}$ by a combination of transformations including a translation, stretches and compressions. Type 1: Horizontal Compression $y=\dfrac{a}{x}, \ 0 \lt a \lt 1$ The […] Sketching quadratic graphs are drawn based on $y=x^2$ graph for transforming and translating. Question 1 $f(x) = (x-3)^2$ is drawn and sketch the following graphs by transforming. (a)   $y = f(x)+2$; Transforming upwards by $2$ units (b)   $y=f(x)-3$; Transforming dowanwards by $3$ […]