Utilize the following properties of function f(x) to answer each part 
*

*domain of $f(x)$ is $[-15,20]$

*$f(-5)=-10$

*$f(8)=15$

*$f(20)=50$

*$f$ is increasing on $10<x<20$

*$f$ is constant on $[5,10]$

*$f$ has zeros at $x=-10$ and $x=0$

*$f$ has an absolute minimum at $x=-5$ and an absolute maximum at $x=20$

 A: evaluate $f(9)$
B: determine range of $f(x)$
C: determine average rate of change of $f(x)$ on $-10<x<-5$
D: which value is bigger: $f(-8)$ or $f(15)$?
A: Hints:
A.  $f$ is constant on $[5,10]$.
B.  $f$ has an absolute minimum at $x=-5$ and an absolute maximum at $x=20$
C.  Quotient of $f(-5)-f(-10)$ and $-5-(-10)$
D.  (Edited) Compare $f(-8)$ and $f(15)$, from the properties stated. You don't need an explicit formula.

Added:
$\color{red}{D}$. If also $f$ is continuous and the only zeros of $f$ occurs at $x=-10$ and $x=0$ we have that $f(x)< 0 $ for $-10<x<0$, then $f(-8)<0$; and $f(15)>f(10)$ since $f$ is increasing on $10<x<10$, and $f(10)=15$ cause $f$ is constant on $[5,10]$. Finally
$$f(15)>f(10)=15>0>f(-8).$$
A: I can't tell this is correct but it is what I could think of right now...it may be helpful anyway!
A-Evaluate $f(9)$
Since $f$ is constant on $[5,10]$ and $f(8)=15$
Then $f(9)=15$
B-Determine the range of $f$
Since $f$ has an absolute minimum at $x=-5$ and an absolute maximum at $x=20$
The range is $[f(-5), f(20)] = [-10, 50]$
C: determine average rate of change of $f(x)$ on $-10<x<-5$ 
$f(-5)=-10 and f(-10)=0$
Similar to calculating the slope of a line passing through $(-5,-10)$ and $(-10,0)$, you can calculate rate of change between the 2 points as: $(y2-y1)/(x2-x1)=(0+10)/(-10+5)=10/-5=-2$ 
D: which value is bigger: $f(-8)$ or $f(15)$?
Since $f(-10)=0$ and $f(-5)=-10$ the function is increasing in this interval and $f(-8)$ would be between $0, -10$. On the contrary, $f(15)$ lies on the interval where $f$ is increasing and that interval starts at $f(10)=15$ and ends at $f(20)=50$, so $f(15)$ must be larger than $f(-8)$.
A picture may help (if correct of course!)

