Increasing and Decreasing Function Intervals Practice Problems

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 $x$-axis.
Step 2: According to the definition of a decreasing function, for any $x_1 < x_2$, it must hold true that $f(x_1) > f(x_2)$. 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.

To analyze whether the function in the graph is decreasing, we must understand how the function's behavior is defined by its graph:

• Step 1: Examine the graph. The graph presented is a horizontal line.
• Step 2: Recognize the properties of a horizontal line. Horizontally aligned lines correspond to constant functions because the $y$-value remains the same for all $x$-values.
• Step 3: Define the criteria for a function to be decreasing. A function decreases when, as $x$ increases, the value of $f(x)$ decreases.
• Step 4: Apply this criterion to the horizontal line. Since the $y$-value is constant and does not decrease as $x$ moves rightward, the function is not decreasing.

Therefore, the function represented by the graph is not decreasing.

Let's first remember that a function is increasing if both the X and Y values are increasing simultaneously.

Conversely, a function is decreasing if the X values are increasing while the Y values are decreasing simultaneously.

In the graph shown, we can see that the function is increasing in every domain and therefore the function is increasing for all values of X.

Let's remember that a function is described as increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph, we can see that in the domain $x < 0.6$ the function is increasing, meaning the Y values are increasing.

Remember that a function is increasing if both X values and Y values are increasing simultaneously.

A function is decreasing if X values are increasing while Y values are decreasing simultaneously.

In the graph, we can observe that in the domain $x > 1$ the function is decreasing, meaning the Y values are decreasing.