Since we are asked to identify and interpret multiple properties of the graph, for clarity we will focus on one property at a time.

Linear or Nonlinear

Since the graph consists of $4$ segments that do not lie on the same straight line, the graph is nonlinear.

$x -$ and $y -$ intercepts

Let's consider the given graph of a stock value, where the $x -$ axis represents the time since the opening bell, $h,$ and the $y -$ axis is the price variation in points.

The graph intersects the $y -$ axis at $(0, 0) .$ This means that there was no price variation before opening bell. The graph also intersects the $x -$ axis at about $(3.2, 0)$ and $(4.5, 0) .$ This means that price was equal to the initial one after about $3.2$ hours and $4.5$ hours.

Positive and Negative Parts

The function is positive when the graph is above the $x -$ axis and negative when it is below.

By examining the graph we can determine at what hours the stock's value is higher than or lower than its starting value.

Positive : Negative : 0 < h < 3.2 and h > 4.5 3.2 < h < 4.5

Note that at

x = 0,

x = 3.2,

and

x = 4.5,

the graph is neither positive nor negative. It is zero.

Increasing and decreasing parts

Regardless of whether the graph is positive or negative with respect to the $y -$ axis, it is increasing when it's rising and decreasing when it's falling.

Examining the graph, we can determine at what hours the stock's value increased and decreased.

Increasing : Decreasing : 0 \leq h < 2 and h > 4 2 < h < 4

Note that at

x = 2

and

x = 4

the graph is neither increasing nor decreasing.

Extrema

We can see the relative extrema for this given function by looking at the graph.

When the function goes from increasing to decreasing like at $h = 2,$ or from decreasing to increasing like at $h = 4,$ we have a relative extrema. Here we have that the stock had a local maximum at $2$ hours and a local minimum at $4$ hours.

End behavior

Exercise