Given the two functions $f$ and $h$ such that $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12$ and $h ( x ) = \left\{ \begin{array} { l } \frac { f ( x ) } { x - 3 } , \text { for } x \neq 3 \\ p , \text { for } x = 3 . \end{array} \right.$ (a) Find all zeros of the function $f$. (b) Find the value of $p$ so that the function $h$ is continuous at $x = 3$. Justify your answer. (c) Using the value of $p$ found in (b), determine whether $h$ is an even function. Justify your answer.

Cortisol is a hormone produced by the adrenal glands and can be considered an important marker of physiological stress. In a study conducted with nurses, it was found that the concentration of salivary cortisol on a work day, denoted by $T$, was, on average, 1.59 times the concentration of salivary cortisol on a day off, denoted by $F$.
In this study, the relationship obtained between $T$ and $F$ was
(A) $T = 1.59 + F$
(B) $F = 1.59 + T$
(C) $\dfrac{T}{F} = 1.59$
(D) $\dfrac{F}{T} = 1.59$
(E) $F \cdot T = 1.59$

Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be a function such that $f ( x + y ) = f ( x ) + f ( y )$ for all $x , y \in \mathbb { R }$, and $g : \mathbb { R } \rightarrow ( 0 , \infty )$ be a function such that $g ( x + y ) = g ( x ) g ( y )$ for all $x , y \in \mathbb { R }$. If $f \left( \frac { - 3 } { 5 } \right) = 12$ and $g \left( \frac { - 1 } { 3 } \right) = 2$, then the value of $\left( f \left( \frac { 1 } { 4 } \right) + g ( - 2 ) - 8 \right) g ( 0 )$ is $\_\_\_\_$ .

I. $f ( x ) = 2 x$ II. $f ( x ) = 2 ^ { x }$ III. $f ( x ) = x ^ { 2 }$ Which of these functions satisfy the equation $f ( a + b ) = f ( a ) \cdot f ( b )$ for every real number a and b?
A) Only I
B) Only II
C) I and II
D) I and III
E) II and III