Question
Which function has a greater rate of change than the function represented in the table.
Responses
A y = 4xy = 4x
B y = x + 2y = x + 2
C y = 2x + 3y = 2x + 3
D y = 3x + 4y = 3x + 4
Responses
A y = 4xy = 4x
B y = x + 2y = x + 2
C y = 2x + 3y = 2x + 3
D y = 3x + 4y = 3x + 4
Answers
Answered by
GPT-4o mini
To determine which function has a greater rate of change than the function represented in the table, we need to analyze the form of each given function. The rate of change of a linear function \( y = mx + b \) is denoted by the slope \( m \).
However, since you did not provide the specific function from the table, I cannot directly compare rates of change with that function. I'll assume that the function represented in the table is a linear function.
Here’s the analysis of the options you've given:
1. **A) \( y = 4x \)**: The slope is \( 4 \).
2. **B) \( y = x + 2 \)**: The slope is \( 1 \).
3. **C) \( y = 2x + 3 \)**: The slope is \( 2 \).
4. **D) \( y = 3x + 4 \)**: The slope is \( 3 \).
If the function in the table has a slope less than \( 4 \), then option A would have a greater rate of change. Similarly, if it's less than \( 3 \), then option D would. If it’s less than \( 2 \), then option C would also suffice. If it's less than \( 1 \), then option B would still apply but is the least steep option.
Therefore, without knowing the specific slope of the function in your table, I cannot definitively tell you which option has a greater rate of change. Please provide the function from the table or its slope for more clarity.
However, since you did not provide the specific function from the table, I cannot directly compare rates of change with that function. I'll assume that the function represented in the table is a linear function.
Here’s the analysis of the options you've given:
1. **A) \( y = 4x \)**: The slope is \( 4 \).
2. **B) \( y = x + 2 \)**: The slope is \( 1 \).
3. **C) \( y = 2x + 3 \)**: The slope is \( 2 \).
4. **D) \( y = 3x + 4 \)**: The slope is \( 3 \).
If the function in the table has a slope less than \( 4 \), then option A would have a greater rate of change. Similarly, if it's less than \( 3 \), then option D would. If it’s less than \( 2 \), then option C would also suffice. If it's less than \( 1 \), then option B would still apply but is the least steep option.
Therefore, without knowing the specific slope of the function in your table, I cannot definitively tell you which option has a greater rate of change. Please provide the function from the table or its slope for more clarity.