To compare the functions A and B, let's analyze both of them.
Function A:
\( y = -3x + 2 \)
This is a linear function with a negative slope (-3), which means that it is decreasing.
Function B:
The values provided are:
- For \( x = 1 \), \( y = 4 \)
- For \( x = 2 \), \( y = 6 \)
- For \( x = 3 \), \( y = 8 \)
- For \( x = 4 \), \( y = 10 \)
From these values, we can see that as \( x \) increases, \( y \) also increases. This indicates that Function B is increasing.
Next, we compare the steepness of the functions:
- The slope of Function A is -3.
- To find the slope for Function B, we can calculate the difference in \( y \) values over the difference in \( x \) values. Between consecutive points, the slope is:
For example, from \( (1, 4) \) to \( (2, 6) \):
\( \text{slope} = \frac{6 - 4}{2 - 1} = \frac{2}{1} = 2 \)
Similarly, this can be checked for all intervals, and the slope will consistently be 2.
Now we can summarize:
- Function A is decreasing (slope = -3).
- Function B is increasing (slope = 2).
- The absolute value of the slope of Function A (-3) is greater than the slope of Function B (2), which means Function A is steeper.
Based on these observations, the most accurate comparison is:
Function A is decreasing, while Function B is increasing AND Function A is steeper.
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