Exponential and Logarithmic Functions

Given an exponential function defined by $f(t)=Pe^{rt}$, where $P>0$ and $r<0$, what feature do these constraints on $P$ and $r$ guarantee about $f(t)$?

Which term best describes a function that can be drawn without lifting your pencil off of the paper for its entire domain?

What is necessary for the piecewise function below to be continuous at x=3?

p(x)= $$\begin{cases} ax^{3}-b & ,\text{if } x <3 \\ cx+d & ,\text{if } x\geq3 \end{cases}$$

If $f(x) = \frac{x^2 - x - 6}{x - 3}$ for all $x$ except $x = 3$, what kind of discontinuity exists at $x = 3$?

What happens to the continuity of $f(x)$ if $\\lim_{x \\to c^{-}} f(x) \\neq \\lim_{x \\to c^{+}} f(x)$?

What is the next number in this arithmetic sequence? 12, 17, 22, ...

What is the first term of an arithmetic sequence with a common difference of 4, if its third term is 10?

What is the result when you translate linear function $p(v)=5v+7$ left horizontally by two units and increase its slope fivefold?

Which of the following functions has a removable discontinuity at x=a?

If the graph of the quadratic function $f(x) = x^2$ is reflected over the x-axis and then vertically stretched by a factor of 3, what is the equation of the new function?