Analyzing Linear Function: Determining Decreasing Behavior from Graph

Question

Is the function shown in the graph below decreasing?

yx

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Visually inspect the graph to see if it is consistently sloping downward.
  • Step 2: Apply the definition of a decreasing function.

Now, let's work through each step:
Step 1: Observing the graph, the function's graph is a line moving from the top left to the bottom right. This indicates it slopes downward as we move from left to right across the x x -axis.
Step 2: According to the definition of a decreasing function, for any x1<x2 x_1 < x_2 , it must hold true that f(x1)>f(x2) f(x_1) > f(x_2) . Since the graph shows a line moving downward, this condition is satisfied throughout its domain.

Therefore, the function represented by the graph is indeed decreasing.

The final answer is Yes.

Answer

Yes