Find the absolute extreme values of the function on the interval.
-$$f ( x ) = | x - 5 | , 4 \leq x \leq 9$$
A) absolute maximum is 4 at x = 9; absolute minimum is 0 at x = 5
B) absolute maximum is 1 at x = 4; absolute minimum is 0 at x = 5
C) absolute maximum is -1 at x = 4; absolute minimum is 4 at x = 9
D) absolute maximum is 4 at x = 9; absolute minimum is 1 at x = 4

Question

Quizplus · Accepted Answer

Since $4\leq x\leq 9$, we only need to consider $x=4$, $x=5$, and $x=9$. 
When $x=4$, we have $f(4)=|4-5|=1$. 
When $x=5$, we have $f(5)=|5-5|=0$. 
When $x=9$, we have $f(9)=|9-5|=4$. 
Therefore, the absolute minimum occurs at $x=5$ with a value of 0, and the absolute maximum occurs at $x=9$ with a value of 4. Thus, the correct choice is $\boxed{	extbf{(A)}}$.

Find the Absolute Extreme Values of the Function on the Interval