Tag Archives: Transformation

Reflections of Graphs

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

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 […]