$$f ( x ) = \left\{ \begin{array} { l l l } 10 - x ^ { 2 } & , & x < 0 \\ a x + b & , & 0 \leq x \leq 3 \\ ( 1 - x ) ^ { 2 } & , & x > 3 \end{array} \right.$$
The function is continuous on the set of real numbers.
Accordingly, what is the sum $\mathbf { a } + \mathbf { b }$?
A) 16 B) 15 C) 12 D) 9 E) 8

Let a be a real number. A function f is defined on the set of real numbers as
$$f ( x ) = \left\{ \begin{array} { c c c } a - x & , & x < 1 \\ 5 x - 4 & , & 1 \leq x \leq 5 \\ ( x - a ) ^ { 2 } + 12 & , & x > 5 \end{array} \right.$$
If there is only one point where the function f is not continuous, what is the value of
$$f ( 7 ) - f ( 0 )$$?
A) 3
B) 4
C) 5
D) 6
E) 7