Question

refer to the graph of f shown below. the xy - coordinate plane is given. the curve labeled f begins at the closed point (1, 0), goes up and right becoming less steep, changes direction at the point (2, 7), goes down and right becoming more steep, passes through the point (3, 4), goes down and right becoming less steep, changes direction at the point (4, 2), goes up and right becoming more steep, passes through the approximate point (4.6, 4), goes up and right becoming less steep, changes direction at the point (5, 6), goes down and right becoming more steep, passes through the point (6, 4), and stops at the closed point (7, 0). (a) if f is increasing on an interval, then the y - values of the points on the graph rise as the x - values increase. from the graph of f we see that f is increasing on the intervals (1,2)∪(4,5). (enter your answer using interval notation.) (b) if f is decreasing on an interval, then the y - values of the points on the graph fall as the x - values increase. from the graph of f shown above, we see that f is decreasing on the intervals. (enter your answer using interval notation.)

Explanation:

Step1: Recall decreasing - function property

A function is decreasing when $y$ - values fall as $x$ - values increase.

Step2: Analyze the graph

We look at the intervals where the graph of $y = f(x)$ is going down as we move from left - to - right. The graph goes down from $x = 2$ to $x = 4$ and from $x = 5$ to $x = 7$.

Step3: Write in interval notation

The intervals are $(2,4)\cup(5,7)$.

Answer:

$(2,4)\cup(5,7)$