Variation of a Function: Drawing conclusions from a table or graph

The problem presents us with a graph of a function, and we need to determine if the function is increasing, decreasing, or constant. An increasing function would show a line rising as you move from left to right, while a decreasing function would show a line falling. A constant function would be represented by a horizontal line on the graph.

Upon examining the graph provided, we observe that the line is horizontal. This means that the y-value of the function does not change regardless of the x-value. The horizontal nature of the line indicates that the function’s output remains the same across its domain, implying that there is neither an upward nor downward trend.

In this scenario, where the graphical line does not incline or decline, the function is determined to be constant. Thus, the correct answer for this problem, based on the graphical representation, is that the function is constant.

Therefore, the solution to the problem is the function is constant.

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

• Step 1: Carefully observe the given graph of $f(x)$.
• 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 $x$ increases, the function's value $f(x)$ decreases.

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

To solve this problem, we will analyze the graph given:

• Step 1: Identify starting condition. Bowl B initially has 32 liters.
• Step 2: Use the graph to track the line for bowl B. This line starts at the point (0, 32) on the graph.
• Step 3: Locate the point where this line intersects with the horizontal line representing 64 liters.
• Step 4: From this intersection point, read down to the time axis to find the corresponding time value.

From the graph, bowl B reaches 64 liters at t = 10 minutes.

Therefore, the correct number of minutes after the taps are opened for bowl B to contain 64 liters of water is 10 minutes.

To solve this problem, we will analyze the graph provided:

The problem states that bowl A starts empty and we need to find out when it reaches 24 liters of water. Observing the graph:

• The line representing bowl A starts at 0 liters.
• Locate the point where the line meets the 24-liter mark on the vertical scale (y-axis).
• From this intersection, move down vertically to the horizontal scale (x-axis) to read the corresponding time in minutes.

According to the graph, when bowl A contains 24 liters of water, the corresponding time is 10 minutes.

Therefore, the answer to the problem is $10$ minutes.

We start by interpreting the graph to find the water levels in bowls A and B at 10 minutes:

• Initially, Bowl A contains 0 liters, and Bowl B contains 32 liters of water.
• According to the graph, as time progresses, both bowls experience changes in water levels.
• After 10 minutes, check the vertical representation on the graph for the water level in each bowl.
• From the graph’s intersection at the 10-minute mark:
• Bowl A shows approximately 24 liters.
• Bowl B shows approximately 64 liters.

We confirm these values against the provided answer options.

Thus, after 10 minutes of pumping water, Bowl A contains $24$ liters, and Bowl B contains $64$ liters.

Therefore, the solution to the problem is $A:24, B:64$.

To solve this problem, let's follow these steps:

• Step 1: Identify the line corresponding to bowl B on the graph. This is typically marked and will indicate the initial amount of water (32 liters).
• Step 2: Observe the line's trajectory as time proceeds. Bowl B starts with 32 liters, so we look for the line that begins at this level on the vertical axis.
• Step 3: The graph line for bowl B will gradually increase as time passes through minute intervals. Find the time at which this line reaches the top level, signifying maximum capacity (full).

Upon examining the graph:

Bowl B's line starts at 32 liters and continues to rise. At the 20-minute interval mark on the time axis, the trajectory for bowl B reaches its peak level and levels off, indicating the bowl is full.

Therefore, the solution to the problem is $20$ minutes.

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

• Step 1: Identify the given information and analyze the graph to understand the data.
• Step 2: Determine which line corresponds to Bowl A and find where it reaches maximum filling on the graph.
• Step 3: Note the time at which the line reaches maximum capacity to solve when Bowl A is full.

Now, let's work through each step:

Step 1: We start by examining the graph. The graph shows two lines, one for each bowl. The vertical axis indicates the amount of water, while the horizontal axis indicates time in minutes.

Step 2: Identify the line that represents Bowl A. From the graph, we find that the line starting at zero represents Bowl A since Bowl B starts at 32 liters.

Step 3: We observe that the line for Bowl A reaches its maximum level on the graph at a time corresponding to 20 minutes. At this point, the line becomes horizontal, indicating the bowl is full.

Therefore, the solution to the problem is 20 minutes.

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

• Step 1: Locate the points on the graph corresponding to 20 and 22 minutes on the time axis.

• Step 2: Identify the water level at 20 minutes.

• Step 3: Identify the water level at 22 minutes.

• Step 4: Compare these two water levels to determine if there is an increase or decrease.

Now, let's work through these steps:

The graph shows the relationship between time and the amount of water in a container. At 20 minutes, the graph indicates a certain water level. By tracing to 22 minutes, we observe the level has changed.

Inspecting the segment from the graph between 20 and 22 minutes, we notice that the line is sloping downwards, indicating a decrease in the amount of water.

This observation shows us that the amount of water decreased between 20 and 22 minutes.

Therefore, the solution to the problem is Decreased.

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

• Step 1: Analyze the given graph to identify the peak point.
• Step 2: Determine the time (in minutes) corresponding to this peak point.

Now, let's work through each step:
Step 1: Upon examining the graph carefully, we identify a clear peak at a particular point. This point represents the maximum amount of water in the container.
Step 2: The peak on the graph is located at approximately the 18-minute mark on the time axis. This represents the moment when the water volume is at its maximum.

Therefore, the greatest amount of water in the container occurs at $18$ minutes.

To solve this problem, we need to read and interpret the provided graph that represents the amount of water in a container as a function of time. Let's follow these steps:

• Step 1: Locate the x-coordinate time value of 14 on the x-axis, which represents the time in minutes.
• Step 2: Find the corresponding point on the graph directly above this x-coordinate.
• Step 3: Read the y-coordinate from the graph at this point, which represents the amount of water in the container.

From the graph, at 14 minutes, the point on the graph lines up with the y-coordinate of 160. This means, at 14 minutes, there are 160 units of water in the container. We are assuming a constant graph scaling and spacing for accurate reading.

Therefore, the solution to the problem is $160$.