# 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} \displaystylef(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 same axes, sketch the graphs of […] # 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: Vertical Compression $y=\dfrac{a}{x}, \ 0 \lt a \lt 1$ The […] # Translations of Graphs

Translation Rule 1 For $y=f(x)+b$, the effect of $b$ is to translate the graph vertically through $b$ units. Translation Rule 2 For $y=f(x-a)$, the effect of $a$ is to translate the graph horizontally through $a$ units. Translation Rule 3 For $y=f(x-a)+b$, the graph is translated $a$ units horizontally and vertically $b$ units. Example 1 Given […] 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 $3$ […]