Question
Compare the functions:
y=-3x+2
x 1,2,3,4
y 4,6,8,10
Function A is decreasing, and Function B is also decreasing AND Function A is steeper
Function A is decreasing, while Function B is increasing AND Function B is steeper
Function A is decreasing, while Function B is increasing AND Function A is steeper
Function A is increasing, while Function B is decreasing AND Function B is steeper
y=-3x+2
x 1,2,3,4
y 4,6,8,10
Function A is decreasing, and Function B is also decreasing AND Function A is steeper
Function A is decreasing, while Function B is increasing AND Function B is steeper
Function A is decreasing, while Function B is increasing AND Function A is steeper
Function A is increasing, while Function B is decreasing AND Function B is steeper
Answers
GPT-4o mini
Let's analyze the functions given:
1. **Function A**: \( y = -3x + 2 \)
- This is a linear function with a slope of \(-3\). Since the slope is negative, Function A is decreasing.
2. **Function B**: Let's consider the set of points given for Function B:
- \( x = 1 \) gives \( y = 4 \)
- \( x = 2 \) gives \( y = 6 \)
- \( x = 3 \) gives \( y = 8 \)
- \( x = 4 \) gives \( y = 10 \)
The values of \( y \) increase as \( x \) increases, indicating that Function B is increasing.
Now, let's summarize the characteristics of both functions:
- **Function A** is decreasing (slope = -3).
- **Function B** is increasing (the values of \( y \) are rising).
Next, we need to determine the steepness of the functions:
- The steepness of a linear function is determined by its slope:
- For Function A, the slope is -3.
- For Function B, we can find its slope using the two points given. The change in \( y \) for the change in \( x \) (between any two points) gives us the slope. For example:
- From the point (1, 4) to (2, 6):
- \( \text{slope} = \frac{6 - 4}{2 - 1} = 2 \)
So we can say:
- Function A (slope = -3) is decreasing.
- Function B (slope = 2) is increasing.
Finally, comparing the steepness:
- Function A is "steeper" than Function B in terms of decline (more negative slope) while Function B is increasing, and since the absolute value of -3 (the slope of Function A) is greater than the slope of Function B (2), this holds true.
Based on the descriptions and definitions:
- Function A is decreasing, while Function B is increasing, and Function A is steeper.
Thus, the correct answer is:
**Function A is decreasing, while Function B is increasing AND Function A is steeper**.
1. **Function A**: \( y = -3x + 2 \)
- This is a linear function with a slope of \(-3\). Since the slope is negative, Function A is decreasing.
2. **Function B**: Let's consider the set of points given for Function B:
- \( x = 1 \) gives \( y = 4 \)
- \( x = 2 \) gives \( y = 6 \)
- \( x = 3 \) gives \( y = 8 \)
- \( x = 4 \) gives \( y = 10 \)
The values of \( y \) increase as \( x \) increases, indicating that Function B is increasing.
Now, let's summarize the characteristics of both functions:
- **Function A** is decreasing (slope = -3).
- **Function B** is increasing (the values of \( y \) are rising).
Next, we need to determine the steepness of the functions:
- The steepness of a linear function is determined by its slope:
- For Function A, the slope is -3.
- For Function B, we can find its slope using the two points given. The change in \( y \) for the change in \( x \) (between any two points) gives us the slope. For example:
- From the point (1, 4) to (2, 6):
- \( \text{slope} = \frac{6 - 4}{2 - 1} = 2 \)
So we can say:
- Function A (slope = -3) is decreasing.
- Function B (slope = 2) is increasing.
Finally, comparing the steepness:
- Function A is "steeper" than Function B in terms of decline (more negative slope) while Function B is increasing, and since the absolute value of -3 (the slope of Function A) is greater than the slope of Function B (2), this holds true.
Based on the descriptions and definitions:
- Function A is decreasing, while Function B is increasing, and Function A is steeper.
Thus, the correct answer is:
**Function A is decreasing, while Function B is increasing AND Function A is steeper**.