Look at the table and choose “true” or “false”.

Question

x y
​​​​​​​1 1
2 4
3 9
4 16
5 25
(5 points)
True False
This table shows a constant rate of change.

This table represents a function.

This table shows an increasing relationship.

This table shows a linear relationship.

This table shows a proportional relationship.

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Answer 1

Let's evaluate each statement based on the data provided in the table.

1. This table shows a constant rate of change.
   False - The rate of change is not constant. The differences between the values of \(y\) are 3, 5, 7, and 9, which are increasing.

2. This table represents a function.
   True - Each input \(x\) has a unique output \(y\), which satisfies the definition of a function.

3. This table shows an increasing relationship.
   True - As \(x\) increases, \(y\) also increases.

4. This table shows a linear relationship.
   False - The relationship is not linear; it is quadratic since \(y = x^2\).

5. This table shows a proportional relationship.
   False - A proportional relationship would require \(y\) to be a constant multiple of \(x\), which is not the case here.

Here are the answers summarized:

• This table shows a constant rate of change: False
• This table represents a function: True
• This table shows an increasing relationship: True
• This table shows a linear relationship: False
• This table shows a proportional relationship: False

Answer 2

relation 1 relation 2 relation 3 relation 4
x y x y x y x y
3 3 5 31 2 3 7 10
4 5 6 28 3 3 8 20
5 7 7 25 4 3 9 30
5 9 8 22 5 3 9 40
6 11 9 19 6 3 10 50
Looking at the 4 tables, answer the following questions.

(3 points)
A. Which table(s) do not represent a function? Response area

B. Which table(s) represent a linear relationship? Response area

C. Which table(s) show a decreasing relationship? Response area

responses
relation 2 and 3
relation 1
relation 2
relation 2 and 4
relation 3 and 4
relation 1 and 4
relation 3
relation 4
relation 1 and 2

Answer 3

Let's analyze each relation based on the given questions:

A. Which table(s) do not represent a function?

For a relation to be a function, each input \(x\) must correspond to exactly one output \(y\).

• Relation 1: \(x = 5\) corresponds to two \(y\) values (7 and 9). Not a function.
• Relation 2: All \(x\) values are unique. Function.
• Relation 3: All \(x\) values are unique. Function.
• Relation 4: All \(x\) values are unique. Function.

Answer: Relation 1.

B. Which table(s) represent a linear relationship?

A linear relationship shows a constant rate of change. We can examine the differences in \(y\) values for each relation.

• Relation 1: Increments by 2 (3, 5, 7, 9, 11) – Linear.
• Relation 2: Increments by -3 for each increase in \(x\), not constant. – Not linear.
• Relation 3: All \(y\) values are constant (3) – Linear, as it can be seen as a horizontal line.
• Relation 4: Increments by 10 (10, 20, 30, 40, 50) – Linear.

Answer: Relation 1, Relation 3, and Relation 4.

C. Which table(s) show a decreasing relationship?

We can examine the trend in \(y\) for each relation.

• Relation 1: Increases – Not decreasing.
• Relation 2: Decreases (31, 28, 25, 22, 19). – Decreasing.
• Relation 3: Constant (3) – Not decreasing.
• Relation 4: Increases (10, 20, 30, 40, 50) – Not decreasing.

Answer: Relation 2.

Summary of Answers:

• A: Relation 1.
• B: Relation 1, Relation 3, and Relation 4.
• C: Relation 2.

Answer 4

This graph shows the progress of a student riding his bike from home to the ice cream shop.



Which 2 statements are true about his journey?

(2 points)
Responses

The student spent more time resting than riding his bike.
The student spent more time resting than riding his bike.

The student stopped for at least one rest break.
The student stopped for at least one rest break.

The student rode faster at the end of his ride than at the beginning.
The student rode faster at the end of his ride than at the beginning.

The student rode faster at the beginning, rested, then a little slower pace, rested, and then a little faster pace.
The student rode faster at the beginning, rested, then a little slower pace, rested, and then a little faster pace.

The student rode slower, then a bit faster, then rested at the ice cream shop.
The student rode slower, then a bit faster, then rested at the ice cream shop.
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Answer 5

To accurately respond to the statements about the student’s bike journey to the ice cream shop, we would need to analyze the details of the graphical representation (like the slope of the lines, the time spent at each point, and any flat sections indicating rest). Since I can’t see the graph, I'll guide you on how to evaluate the statements based on typical patterns seen in such graphs.

1. The student spent more time resting than riding his bike.

   • You would look for long horizontal segments in the graph where the student is not moving (indicating rest). If those segments are longer than the riding segments, this statement would be true. Otherwise, it would be false.

2. The student stopped for at least one rest break.

   • If the graph shows any flat sections (horizontal lines), it indicates pauses or rests. If you see at least one of these sections, this statement would be true.

3. The student rode faster at the end of his ride than at the beginning.

   • You could determine this by analyzing the slopes of the lines at the start versus the end. If the line's slope is steeper at the end than at the beginning, this statement would be true.

4. The student rode faster at the beginning, rested, then a little slower pace, rested, and then a little faster pace.

   • This statement would involve analyzing the slopes for speed variations and spotting rests. If the graph indicates this pattern, this statement would be true.

5. The student rode slower, then a bit faster, then rested at the ice cream shop.

   • Similarly, you would check if there is a general slow start, followed by a speed increase, and then a flat section (for resting) at the end. If this is how the graph looks, this statement would be true.

Conclusion

Without being able to see the graph, the evaluation would be based on how the graph appears, regarding resting sections and speed changes. Look for the mentioned characteristics to determine the two true statements from the options provided. If you can describe the graph or share any observations, I can further assist in confirming which statements are true.

Answer 6

choose two answers

Answer 7

Without viewing the actual graph, I can guide you based on typical patterns observed in bike ride graphs. If I had to suggest two statements that are commonly true for a student riding a bike with rests, they would likely align with the following assumptions.

Based on typical behaviors and without specifics from the graph, you can generally choose:

1. The student stopped for at least one rest break.

   • This is often true in scenarios where a student might need to pause during a longer ride.

2. The student rode faster at the beginning, rested, then a little slower pace, rested, and then a little faster pace.

   • This pattern also represents a common biking behavior, where riders start strong, take breaks, and then have variations in speed.

So the suggested answers would be:

• The student stopped for at least one rest break.
• The student rode faster at the beginning, rested, then a little slower pace, rested, and then a little faster pace.

Please apply your judgment based on the graph provided to make the best choice considering what you see there!

Answer 8

This graph shows a student’s distance from home over time.

Which 2 statements best describe the student’s journey?

(2 points)
Responses

The student left home and never came back during this journey.
The student left home and never came back during this journey.

The student left and came back home twice on this journey.
The student left and came back home twice on this journey.

The student rested 3 times during his journey.
The student rested 3 times during his journey.

The student went further away from home each time he left the house.
The student went further away from home each time he left the house.

The student went up and down the neighborhood looking for his dog.
The student went up and down the neighborhood looking for his dog.

The student climbed 3 hills during his journey.
The student climbed 3 hills during his journey.
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Answer 9

To select the best two statements that describe the student's journey based on the graph of distance from home over time, consider the following possibilities:

1. The student left home and never came back during this journey.

   • This would be true if the graph shows a continuous increase (moving away from home) without any return to the initial position.

2. The student left and came back home twice on this journey.

   • This would be true if the graph shows at least two instances where the distance returns to zero, indicating the student returned home.

3. The student rested 3 times during his journey.

   • This would be true if the graph shows three flat segments where the student is stationary (indicating rests).

4. The student went further away from home each time he left the house.

   • This would be true if there are no instances of the student returning home or if each departure point is further than the last.

5. The student went up and down the neighborhood looking for his dog.

   • This might be true based on the graph showing up and down movements (suggesting a back-and-forth journey).

6. The student climbed 3 hills during his journey.

   • This would be true if the graph shows three clear upward segments followed by downward segments (indicating hills).

Suggested Answers:

Based on common scenarios seen in graphs of distance over time, I would likely suggest:

• The student left and came back home twice on this journey. (if there are two returns to the starting point in the graph)
• The student rested 3 times during his journey. (if there are three flat segments that suggest resting)

If the graph depicts a different behavior, adjust accordingly based on the information it provides. Please choose the statements that best match what you see in the graph.

Answer 10

Look at the Graphs a, b, and c. Answer the questions.

(4 points)
A. Which graph(s) are not a function? (Response area)

B. Why are the graph(s) NOT a function? (Response area)

C. Which graph(s) are NOT Linear? (Response area)

D. Which graph(s) have a constant rate of change? (Response area)

responses
graph a
graph b
graph c
graph a and c
graph b and c
graph a and b
because each input does not have exactly one output
because each output does not have exactly one input
because it is not linear
because the graph increases and decreases

Answer 11

To address the questions about Graphs A, B, and C, I'll provide guidance on how to determine the answers based on the typical characteristics of graphs. Since I cannot see the graphs, I will describe how you might evaluate each question:

A. Which graph(s) are not a function?

• To determine whether a graph represents a function, you can apply the Vertical Line Test: If a vertical line crosses the graph at more than one point, then the graph does not represent a function.

Possible Responses:

• If any of the graphs fail the vertical line test, you would indicate those graphs.
• Response could be: graph a, graph b, or graph c depending on which ones fail the test.

B. Why are the graph(s) NOT a function?

• If a graph is not a function, it's typically due to each input (x-value) not having exactly one output (y-value). In mathematical terms:
  • Response: because each input does not have exactly one output.

C. Which graph(s) are NOT Linear?

• A linear graph is represented by a straight line. If a graph is curved, it is not linear.

Possible Response:

• Indicate graph(s) that are curved.
• Response could be: graph a, graph b, or graph c based on which ones are not straight lines.

D. Which graph(s) have a constant rate of change?

• A graph has a constant rate of change if it is linear (a straight line). A linear graph maintains the same slope throughout.

Possible Response:

• Indicate which of the graphs are linear.
• Response could be: graph a, graph b, or graph c depending on which ones are straight lines.

Summary of Possible Answers:

Without the visual context of the graphs, you would choose:

• A: Graph(s) that do not represent a function.
• B: Because each input does not have exactly one output.
• C: Graph(s) that are not linear.
• D: Graph(s) that have a constant rate of change.

You would select responses based on the characteristics you observe in the graphs. Please match the answers according to what you see in graphs A, B, and C.