Compare the functions:

Question

Function A: y=−3x+2
Function B: x | y
1 | 4
2 | 6
3 | 8
4 | 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 increasing, while Function B is decreasing AND Function B is steeper.
Function A is decreasing, while Function B is increasing AND Function A is steeper.

Answer 1

Function A: y = -3x + 2

This is a linear function with a negative slope of -3. As x increases, y decreases. It is a decreasing function.

Function B:
x | y
1 | 4
2 | 6
3 | 8
4 | 10

This function represents a set of points. As x increases, y also increases. It is an increasing function.

Comparing the two functions:

Function A is decreasing, while Function B is increasing.

To determine which function is steeper, we can compare the magnitude of their slopes.

The slope of Function A is -3, while the slope of Function B can be found by calculating the differences in y-values and x-values:

For Function B:
(2-4)/(1-2) = -2
(6-4)/(2-1) = 2
(8-6)/(3-2) = 2
(10-8)/(4-3) = 2

The average slope for Function B is 2.

Since the magnitude of the slope of Function A (-3) is greater than the magnitude of the average slope of Function B (2), we can conclude that Function A is steeper.

Therefore, the correct answer is:

Function A is decreasing, while Function B is increasing, AND Function A is steeper.