Question
Question
Use the image to answer the question.
Function 1: f(x)=3/2x+5
Function 2:
A diagonal line connects two data points on a coordinate plane.
Which function has the greater rate of change?
Type 1 for Function 1.
Type 2 for Function 2.
(1 point)
Function
Use the image to answer the question.
Function 1: f(x)=3/2x+5
Function 2:
A diagonal line connects two data points on a coordinate plane.
Which function has the greater rate of change?
Type 1 for Function 1.
Type 2 for Function 2.
(1 point)
Function
Answers
Answered by
GPT-4o mini
To determine which function has the greater rate of change, we need to analyze the slopes of both functions.
For Function 1, given as \( f(x) = \frac{3}{2}x + 5 \), the slope (rate of change) is \( \frac{3}{2} \).
Function 2 is described as a diagonal line connecting two data points. The rate of change for a linear function is determined by its slope, which is calculated as the change in y divided by the change in x (rise over run).
Without specific information about the coordinates of the two data points for Function 2, we cannot compute its slope directly. However, if we assume that the line is less steep than Function 1, the slope would be less than \( \frac{3}{2} \).
If the information on Function 2 shows that it has a slope greater than \( \frac{3}{2} \), then it would have a greater rate of change. Given this lack of specific data, if we judged based solely on the known slope of Function 1:
Thus, based on the comparison of slopes:
- If Function 2’s slope is less than \( \frac{3}{2} \), the answer is 1 (Function 1).
- If Function 2’s slope is \( \frac{3}{2} \) or greater (which is unknown), then the answer would be 2 (Function 2).
Since we can't definitively determine without the coordinates of Function 2, we would choose **1** for Function 1 as the function with the known slope.
The answer is: **1**
For Function 1, given as \( f(x) = \frac{3}{2}x + 5 \), the slope (rate of change) is \( \frac{3}{2} \).
Function 2 is described as a diagonal line connecting two data points. The rate of change for a linear function is determined by its slope, which is calculated as the change in y divided by the change in x (rise over run).
Without specific information about the coordinates of the two data points for Function 2, we cannot compute its slope directly. However, if we assume that the line is less steep than Function 1, the slope would be less than \( \frac{3}{2} \).
If the information on Function 2 shows that it has a slope greater than \( \frac{3}{2} \), then it would have a greater rate of change. Given this lack of specific data, if we judged based solely on the known slope of Function 1:
Thus, based on the comparison of slopes:
- If Function 2’s slope is less than \( \frac{3}{2} \), the answer is 1 (Function 1).
- If Function 2’s slope is \( \frac{3}{2} \) or greater (which is unknown), then the answer would be 2 (Function 2).
Since we can't definitively determine without the coordinates of Function 2, we would choose **1** for Function 1 as the function with the known slope.
The answer is: **1**