Select the graph of the given function and determine the interval(s) for which $f ( x ) \geq 0$
$f ( x ) = 6 - x$
A) $(-\infty, 6]$
B) $( - \infty , - 6 ]$
C) $(-\infty, 6]$
D) $(\infty,-6]$
E) $( \infty , 6 ]$

Question

Select the graph of the given function and determine the interval(s) for which $f ( x ) \geq 0$
$f ( x ) = 6 - x$
A) $(-\infty, 6]$ 
B) $( - \infty , - 6 ]$ 
C) $(-\infty, 6]$ 
D) $(\infty,-6]$ 
E) $( \infty , 6 ]$

Quizplus · Accepted Answer

The graph of the function is a line with a slope of -1 and y-intercept of 6. It decreases linearly from left to right. Therefore, the interval for which $f(x)\geq0$ is from $-\infty$ to the $x$-value where the graph intersects the x-axis, which is 6. So the interval is $(-\infty, 6]$. This matches with choice C.

Select the Graph of the Given Function and Determine the Interval(s)