Analyzing f(x): Determine the Linear Function's Increasing or Decreasing Behavior

Here is a graph of a function. f(x) f(x)

Is the function increasing, decreasing or constant?

111222333444555666777888999101010111111121212111222333444555666000

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine whether the function is increasing, decreasing, or constant?
00:03 For this, let's take several points on the graph and observe the rate of change
00:40 We can see that the Y values are decreasing, therefore the function is decreasing
00:47 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Here is a graph of a function. f(x) f(x)

Is the function increasing, decreasing or constant?

111222333444555666777888999101010111111121212111222333444555666000

2

Step-by-step solution

To solve this problem, we'll analyze the graph of the function:

  • Step 1: Carefully observe the given graph of f(x) f(x) .
  • Step 2: Evaluate the overall trend of the graph.
  • Step 3: Determine if the function is increasing, decreasing, or constant based on the slope.

Now, let's go through the solution:
Step 1: Observing the graph, we see that the curve starts at a higher coordinate on the y-axis and moves downwards as it progresses from left to right.
Step 2: This indicates a negative slope, as the y-values decrease while the x-values increase.
Step 3: Reasoning from the previous observations, it is clear that as x x increases, the function's value f(x) f(x) decreases.

Therefore, the correct conclusion is that the function f(x) f(x) is decreasing.

3

Final Answer

Decreasing

Practice Quiz

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Given the following graph, determine whether function is constant

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