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

1 answer

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.