Question

Question

Compare the functions:

Function A:

y=−3x+2


Function B:
x y
1 4
2 6
3 8
4 10
(1 point)
Responses

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

Answer 1

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."