Question

Identify the end behavior of the following function. f (x) = -x +11+3 As r → -, y → - and as a → 00, Y + -a As x + -, y → and as a → 00, y → As I —-~, y and as x > 0, y 0 As a -∞, y 0, y = -~ and as x > , y → Question 5 (4 points) Evaluate the following piecewise function for x=1. 112-9 il

Answer 1

You have the following function:

f(x) = -|x + 1| + 3

take into account that the absolute value of any positive or negative number is a positive number. Then, if you have the absolute value of -∞, that is, |-∞|, this is equal to ∞, |-∞| = ∞.

Then, if x=> -∞, you obtain:

f(-∞) = -|(-∞) + 1| + 3

f(-∞) = -|-∞| + 3

f(-∞) = -(∞) + 3

f(-∞) = -∞

The same result is obtained when x => ∞:

f(∞) = -|∞ + 1| + 3

f(∞) = -∞ + 3

f(∞) = -∞

Then, you can conclude:

As x => -∞, y => -∞ and as x => ∞, y => -∞ (first option)