4.1 (Function properties) Exercises
PCHA 2021-22 / Dr. Kessner

Graph each of the functions below. Then determine the following properties of the function:

• domain and range
• discontinuities (removable, jump, infinite)
• intervals of increasing/decreasing
• boundedness (above/below)
• local/global extrema
• odd/even symmetry
• asymptotes (with limits)
• end behavior (with limits)

1. $\sin(x), \cos(x), \tan(x), \csc(x), \sec(x), \cot(x)$.

2. $x, x^2, x^3, x^4$

3. $|x|, \dfrac{|x|}{x}$

4. $\sqrt{x}, \sqrt[3]{x}$

5. $\dfrac{1}{x}$

6. $2^x, 10^x$