To compare Functions A and B, let's analyze them individually.
Function A: The equation is given as \( y = -3x + 2 \).
- This is a linear function with a negative slope of -3.
- The negative slope indicates that Function A is decreasing.
Function B: The values of Function B are listed as pairs of \( (x, y) \):
- When \( x = 1 \), \( y = 4 \)
- When \( x = 2 \), \( y = 6 \)
- When \( x = 3 \), \( y = 8 \)
- When \( x = 4 \), \( y = 10 \)
To determine if Function B is increasing or decreasing, we can look at the \( y \)-values as \( x \) increases:
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As \( x \) increases from 1 to 4, the \( y \)-value increases from 4 to 10.
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We can also calculate the slope of Function B, which is: \[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{10 - 4}{4 - 1} = \frac{6}{3} = 2 \]
Thus, Function B has a positive slope (2) and is therefore increasing.
Now, we can summarize the comparison:
- Function A is decreasing (negative slope of -3).
- Function B is increasing (positive slope of 2).
- In terms of steepness, the absolute value of the slope of Function A (3) is greater than that of Function B (2), indicating that Function A is steeper.
Based on this analysis, the correct response is:
Function A is decreasing, while Function B is increasing AND Function A is steeper.