To compare the functions, let's analyze each one.
Function A:
The equation is given as \( y = -3x + 2 \).
- The slope (coefficient of x) is -3. Since the slope is negative, this indicates that Function A is decreasing.
Function B:
The values given for Function B are:
- When \( x = 1 \), \( y = 4 \)
- When \( x = 2 \), \( y = 6 \)
- When \( x = 3 \), \( y = 8 \)
- When \( x = 4 \), \( y = 10 \)
To determine the behavior of Function B, observe the \( y \) values:
- The values of \( y \) increase as \( x \) increases.
- This indicates that Function B is increasing.
Now, we need to determine the steepness or rate of change for both functions.
- Steepness of Function A: The slope is -3.
- Steepness of Function B: Let's calculate the slope using the changes in y-values:
- From \( y = 4 \) to \( y = 6 \) (change of 2 over a change of 1 in x) gives a slope of \( \frac{2}{1} = 2 \).
- The same applies for other points—so the slope for Function B is +2.
Comparing steepness:
- Function A has a slope of -3 (decreasing).
- Function B has a slope of +2 (increasing).
Since we are looking at the absolute values of the slopes for steepness:
- The steepness of Function A is |−3| = 3.
- The steepness of Function B is |2| = 2.
Conclusion:
- Function A is decreasing.
- Function B is increasing.
- Function A is steeper than Function B because 3 > 2.
Therefore, the correct response is:
"Function A is decreasing, while Function B is increasing AND Function A is steeper."
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