Worked Examples in Function Analysis
Here are several examples I’ve worked through, applying tools from mathematical analysis to study and sketch the graphs of various functions:
| Exercise | Function |
|---|---|
| Exercise | $$ f(x) = \frac{x}{1-x} $$ |
| Exercise | $$ f(x) = x^3 - 3x + 2 $$ |
| Exercise | $$ f(x) = \frac{x+1}{x-1} $$ |
| Exercise | $$ f(x) = \frac{x-1}{x+1} $$ |
| Exercise | $$ f(x) = \frac{x^2 + 2}{x} $$ |
| Exercise | $$ f(x) = \frac{x}{x^2 + 2} $$ |
| Exercise | $$ f(x) = \frac{5x - 1}{x^2 - 3x + 2} $$ |
| Exercise | $$ f(x) = \sqrt{x^2 - 16} $$ |
| Exercise | $$ f(x) = e^{\frac{1}{x}} $$ |
| Exercise | $$ f(x) = e^{-\frac{1}{x}} $$ |
| Exercise | $$ f(x) = e^x + e^{-x} $$ |
| Exercise | $$ f(x) = \frac{x}{e^x} = x \cdot e^{-x} $$ |
