Question

Proximate when the function is positive, negative, increasing, or decreasing.

y=x+4-1
-6
-2
2
decreasing:
X
The function is positive:
and
#x<-4 #x>-4
negative:
#x<-5 #x> 3 #-5 increasing:
:: for all real numbers.

Answer 1

To determine when the function y = x + 4 - 1 is positive, negative, increasing, or decreasing, we need to analyze the behavior of the function based on the given values of x: -6, -2, and 2.

1. For x = -6:

Substituting x = -6 into the function, we get y = (-6) + 4 - 1 = -3.

Since the value of y is negative, we can conclude that the function is negative for x = -6.

2. For x = -2:

Substituting x = -2 into the function, we get y = (-2) + 4 - 1 = 1.

Since the value of y is positive, we can conclude that the function is positive for x = -2.

3. For x = 2:

Substituting x = 2 into the function, we get y = 2 + 4 - 1 = 5.

Since the value of y is positive, we can conclude that the function is positive for x = 2.

Based on these calculations, we can summarize the behavior of the function as follows:

- The function is negative for x = -6.

- The function is positive for x = -2 and x = 2.

Regarding the increasing or decreasing behavior, the given function is a linear equation with a coefficient of 1 in front of x. This means that the function has a constant slope of 1, and it is always increasing. Therefore, we can say that the function is increasing for all real numbers.

In conclusion:

- The function is negative for x = -6.

- The function is positive for x = -2 and x = 2.

- The function is always increasing for all real numbers.

Explanation: