Question

Given the piecewise equation: y = {3x + 4 if x ≤ −5, -2x + 6 if 0 < x ≤ 2, -4/3x + 6 if 4 ≤ x}.

a) Find the value of y when x = -5.
b) Find the value of y when x = 2.
c) Find the value of y when x = 4.
d) Determine the domain of the function.

Answer 1

a) When x = -5, y = -11. b) When x = 2, y = 2. c) When x = 4, y = 2/3. d) The domain of the function is -∞ < x ≤ -5, 0 < x < 2, and x ≥ 4.

Step-by-step explanation:

a) To find the value of y when x = -5, substitute x = -5 into the first piece of the equation: y = 3x + 4. Plugging in x = -5, we get y = 3(-5) + 4 = -15 + 4 = -11. Therefore, when x = -5, y = -11.

b) To find the value of y when x = 2, substitute x = 2 into the second piece of the equation: y = -2x + 6. Plugging in x = 2, we get y = -2(2) + 6 = -4 + 6 = 2. Therefore, when x = 2, y = 2.

c) To find the value of y when x = 4, substitute x = 4 into the third piece of the equation: y = -4/3x + 6. Plugging in x = 4, we get y = -4/3(4) + 6 = -16/3 + 6 = -16/3 + 18/3 = 2/3. Therefore, when x = 4, y = 2/3.

d) The domain of the function is the set of all possible x-values. In this piecewise equation, x-values less than or equal to -5, between 0 and 2 (excluding 0 and 2), and greater than or equal to 4 are defined. Therefore, the domain is -∞ < x ≤ -5, 0 < x < 2, and x ≥ 4.