Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.
- $\rhd$ Graphing a rational function (9:57) Find the $x$- and $y$-intercepts, and asymptotes of $f(x)=\dfrac{2x-4}{1-x}$. Sketch the graph.
- $\rhd$ Graphing rational functions according to asymptotes (11:21) Finding the horizontal and vertical asymptotes of $\dfrac{3x^2-18x-81}{6x^2-54}$.
- $\rhd$ Graphs of rational functions: y-intercept (3:07) Given four graphs, identify the graph of the function $f(x)=\dfrac{ax^n+bx+12}{cx^m+dx+12}$ by finding its $y$-intercept.
- $\rhd$ Graphs of rational functions: horizontal asymptote (3:15) Given four graphs, identify the graph of the function $f(x)=\dfrac{-x^2+ax+b}{x^2+cx+d}$ by finding its horizontal asymptote.
- $\rhd$ Graphs of rational functions: vertical asymptote (5:33) Given four graphs, identify the graph of the function $f(x)=\dfrac{g(x)}{x^2-x-6}$ where $g(x)$ is a polynomial by finding its vertical asymptote.
- $\rhd$ Graphs of rational functions: zeros (7:46) Given four graphs, identify the graph of the function $f(x)=\dfrac{3x^2-18}{g(x)}$ where $g(x)$ is a polynomial by finding its zeros.
- * Practice problem: Type of problem: Identify the graph of $\dfrac{15x^3+b}{3x^3+cx+d}$ where $b$, $c$ and $d$ are unknown constants.
