Question

Function A:
y = -3x + 2

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

compare these functions
Responses:
Function A is increasing, while Function B is decreasing 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.
Function A is decreasing, while Function B is increasing AND Function A is steeper.

Function A is decreasing and Function B is also decreasing AND Function A is steeper.
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.

Answer 1

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:
- As \( x \) increases from 1 to 4, the \( y \)-value increases from 4 to 10.

- 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.**