If $f(x) = ax + b$, where $a$ and $b$ are integers, $f(-1) = -5$, and $f(3) = 3$, then $a$ and $b$ are respectively:

Let $R$ be the set of real numbers. Define the real function $f: R \rightarrow R$ by $f(x) = x + 10$ and sketch the graph of this function.

The minimum value of $|x| + |x + \frac{1}{2}| + |x - 3| + |x - \frac{5}{2}|$ is

For a real number $x$,let $[x]$ denote the greatest integer less than or equal to $x$,and let $\{x\} = x - [x]$. The number of solutions $x$ to the equation $[x]\{x\} = 5$ with $0 \leq x \leq 2015$ is

Let the function $g : (-\infty, \infty) \to \left( - \frac{\pi}{2}, \frac{\pi}{2} \right)$ be given by $g(u) = 2 \tan^{-1}(e^u) - \frac{\pi}{2}$. Then,$g$ is -

Number of solutions of the equation $2^x + x = 2^{\sin x} + \sin x$ in $[0, 10\pi]$ is -