Functions - Examples, Exercises and Solutions

Let's remember that the function increases if the $x$ values and $y$ values increase simultaneously.

On the other hand, the function decreases if the $x$ values increase while the $y$ values decrease simultaneously.

In the given graph, we can see that the function increases in the domain where x > 0 ; in other words, where 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.

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 the function increases if the X values and Y values increase simultaneously.

On the other hand, the function decreases if the X values increase and the Y values decrease simultaneously.

In the given graph, we notice that the function increases in the domain where x < 0 , meaning the Y values are increasing.

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.

To solve this problem, we'll begin by examining the graph of the function provided:

• Step 1: Observe the graph from left to right along the x-axis.
• Step 2: Look for any intervals where the function value (y-coordinate) does not decrease as the x-value increases.
• Step 3: Pay special attention to segments where the graph might look horizontal or rising.

Upon inspecting the graph, we find:

- There are sections where the function's y-values appear to remain constant or potentially rise as the x-values increase. Specifically, even if the function decreases in major portions, any interval where it doesn't means the function cannot be classified as decreasing throughout.

Thus, the function does not strictly decrease on the entire interval shown. Therefore, the solution to the problem is No.

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

• Step 1: Verify the graph's overall path direction
• Step 2: Confirm if the y-values are decreasing as we proceed from the left side of the graph to the right side (increasing x-values).

Now, let's work through each step:

Step 1: By examining the graph, the red line starts at a higher point on the y-axis and moves downward to a lower point as it moves horizontally across the x-axis from left to right.

Step 2: Since for every point, the red line descends as it progresses from the leftmost point to the rightmost, this indicates a consistent decrease in the y-values.

Therefore, the solution to the problem is Yes, the function in the graph is decreasing.

The graph presented is a straight line. To determine whether the function is decreasing, we need to examine the slope of this line.

The line has a negative slope, as it moves downward from left to right. A function is considered decreasing when its slope is negative.

In formal terms, for a linear function expressed as $y = mx + c$, if the slope $m$ is negative, the function is decreasing over its entire domain.

From the graph, it's evident that the line has a negative slope, thus indicating that the function is indeed decreasing.

Therefore, the answer to the problem 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.

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.

The function increases if X values and Y values increase simultaneously.
In this function, despite its unusual form, we can observe that the function continues to increase according to the definition at all times,
Furthermore there is no stage where the function decreases.
Therefore, we can say that the function increases for all X, there is no X we can input where the function will be decreasing.

Remember that a function is increasing if both the $x$ values and the $y$ values are increasing simultaneously.

A function is decreasing if the $x$ values are increasing while the $y$ values are decreasing simultaneously.

In the graph we can see that the function is decreasing in all domains. In other words, it is decreasing for all $x$.

Remember that a function is increasing if the $x$ values and $y$ values are increasing simultaneously.

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

In the plotted graph, we can see that in the domain 1.1 > x > 0 the function is increasing—meaning the $y$ values are increasing.

According to logic, the student's grades throughout the year depend on many criteria that are not given to us.

Therefore, the appropriate domain for the function is - it is impossible to know.

According to logic, the speed of the stone during a fall from a great height will increase as it falls with acceleration.

In other words, the speed of the stone increases, so the appropriate domain for this function is - always increasing.