Answer:
To understand the positive and negative values of the function f(x) = 3|x| + 5 and whether it's increasing or decreasing, let's break it down:
Positive and Negative Values:
When x is positive (greater than or equal to 0), f(x) = 3x + 5 because the absolute value of a positive number is itself.
When x is negative (less than 0), f(x) = 3(-x) + 5 because the absolute value of a negative number is its positive counterpart.
Therefore, for positive x values, f(x) is positive, and for negative x values, f(x) is also positive.
Increasing or Decreasing:
To determine if the function is increasing or decreasing, we can look at its slope (the coefficient of x). If the coefficient of x is positive, the function is increasing; if it's negative, the function is decreasing.
In this case, the coefficient of x is 3, which is positive. So, the function f(x) = 3|x| + 5 is increasing for all real values of x.
In summary:
The function is positive for both positive and negative values of x.
The function is increasing for all real values of x.