which shows a function that is decreasing over its entire graph?

Explanation:

Step1: Recall definition of decreasing function

A function is decreasing over its entire graph if for any two points $(x_1,y_1)$ and $(x_2,y_2)$ where $x_2>x_1$, then $y_2 < y_1$.

Step2: Analyze each graph

• First graph: It is a V - shaped graph (absolute - value function), which has a decreasing part and an increasing part.
• Second graph: As we move from left to right (increase in $x$ - values), the $y$ - values are always getting smaller.
• Third graph: It has an increasing part and a decreasing part.
• Fourth graph: It is a vertical line, which is not a function (fails the vertical - line test).

Answer:

The second graph.