Question

Question 1

The table shows the age relationship between Jamie's cat and dog.

Which equation gives this relationship? Let c represent the cat's age and d represent the dog's age.
Responses
A c = d + 4c = d + 4
B d = c + 4d = c + 4
C c = d + 3c = d + 3
D d = c + 3

Answer 1

[AI-generated answer — Bot GPT 3.5]

A) c = d + 4

Answer 2

how do you know?

Answer 3

[AI-generated answer — Bot GPT 3.5]

We know that c represents the cat's age and d represents the dog's age. The table shows the age relationship between the cat and dog, and we need to find the equation that represents this relationship. In the table, the cat's age is always 4 years older than the dog's age. This can be represented by the equation c = d + 4, where c is the cat's age and d is the dog's age.

Answer 4

this is the graph

Cat (c) Dog (d)
1 4
2 5
3 6
4 7

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the confusion. Based on the given graph, we can determine the equation by observing the pattern of the relationship between the cat's age (c) and the dog's age (d).

Looking at the table, we can see that the difference between the cat's age and the dog's age is always 3. In other words, the cat's age is always 3 years less than the dog's age.

Therefore, the correct equation that represents this relationship is:

c = d - 3

So the correct answer is:

D) d = c + 3

Answer 6

Which relation describes a function?

Responses
A {(0, 0), (0, 2), (2, 0), (2, 2)}
{(0, 0), (0, 2), (2, 0), (2, 2)}
B {(−2, −3), (−3, −2), (2, 3), (3, 2)}{(−2, −3), (−3, −2), (2, 3), (3, 2)}
C {(2, −1), (2, 1), (3, −1), (3, 1)}
{(2, −1), (2, 1), (3, −1), (3, 1)}
D {(2, 2), (2, 3), (3, 2), (3, 3)}{(2, 2), (2, 3), (3, 2), (3, 3)}
E {(4, 3) , (1, 8) , (4, 14) , (9, 16)}

Answer 7

[AI-generated answer — Bot GPT 3.5]

A relation describes a function if each input has only one output.

Looking at the given options:

A) This relation does not describe a function because both x = 0 and x = 2 have multiple outputs (y = 0 and y = 2).

B) This relation does not describe a function because both x = -2 and x = 3 have multiple outputs (y = -3 and y = 2).

C) This relation does not describe a function because both x = 2 and x = 3 have multiple outputs (y = -1 and y = 1).

D) This relation does describe a function because for each unique x-value, there is only one y-value.

E) This relation does not describe a function because x = 4 has multiple outputs (y = 3 and y = 14).

Therefore, the relation that describes a function is:

D) {(2, 2), (2, 3), (3, 2), (3, 3)}

Answer 8

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05:48

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Linear & Nonlinear Functions

Question 1
Which table of values appears to show a linear function?
Responses
A A onlyA only
B C onlyC only
C A and BA and B
D A and CA and C
Question 2
Which set of values appears to show a nonlinear function?
Responses
A (1, 1), (2, 4), (3, 9), and (4, 16)(1, 1), (2, 4), (3, 9), and (4, 16)
B (2, 5), (3.5, 8), (4, 9), and (4.5, 10)(2, 5), (3.5, 8), (4, 9), and (4.5, 10)
C (1, 2), (2, −1), (4, −7), and (6, −13)(1, 2), (2, −1), (4, −7), and (6, −13)
D (−2, 3), (8, −2), (10, −3), and (20, −8)(−2, 3), (8, −2), (10, −3), and (20, −8)

Answer 9

[AI-generated answer — Bot GPT 3.5]

Question 1: To determine which table appears to show a linear function, we need to look for a consistent rate of change in the y-values for each unit increase in the x-values.

A: A only - The y-values have a consistent rate of change of 2 for each unit increase in the x-values, indicating a linear function.

B: C only - The y-values do not have a consistent rate of change for each unit increase in the x-values, indicating a nonlinear function.

C: A and B - The y-values have a consistent rate of change of 2 for each unit increase in the x-values, indicating a linear function.

D: A and C - The y-values have a consistent rate of change of 2 for each unit increase in the x-values, indicating a linear function.

Based on this analysis, the correct response is:

A) A only

Question 2: To determine which set of values appears to show a nonlinear function, we need to look for a non-constant rate of change in the y-values for each unit increase in the x-values.

A: (1, 1), (2, 4), (3, 9), and (4, 16) - The y-values have a consistent rate of change of 3 for each unit increase in the x-values, indicating a linear function.

B: (2, 5), (3.5, 8), (4, 9), and (4.5, 10) - The y-values do not have a consistent rate of change for each unit increase in the x-values, indicating a nonlinear function.

C: (1, 2), (2, −1), (4, −7), and (6, −13) - The y-values do not have a consistent rate of change for each unit increase in the x-values, indicating a nonlinear function.

D: (−2, 3), (8, −2), (10, −3), and (20, −8) - The y-values do not have a consistent rate of change for each unit increase in the x-values, indicating a nonlinear function.

Based on this analysis, the correct response is:

B) (2, 5), (3.5, 8), (4, 9), and (4.5, 10)

Answer 10

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08:02

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Graph of a Linear Function
Consider the function: y = 8 − 2x.
Question 1
What is the effect on the graph for the given function if the slope of the function is changed to −10?
Responses
A The line shifts up.The line shifts up.
B The line shifts down.The line shifts down.
C The line is more steep.The line is more steep.
D The line is less steep.The line is less steep.
Question 2
What is the effect on the graph for the given function if the y-intercept of the function is changed to a smaller positive number?
Responses
A The line shifts up.The line shifts up.
B The line shifts down.The line shifts down.
C The line is more steep.The line is more steep.
D The line is less steep.The line is less steep.

Answer 11

[AI-generated answer — Bot GPT 3.5]

Question 1: The given function is y = 8 - 2x. The slope of the function determines the steepness of the line. If the slope is changed to -10, the line becomes steeper.

Therefore, the correct response is:

C) The line is more steep.

Question 2: The y-intercept of the function determines the point where the line intersects the y-axis. If the y-intercept is changed to a smaller positive number, the line will shift up.

Therefore, the correct response is:

A) The line shifts up.