Answer:
The function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2.
The vertex of the function is (-2,-1)
Domain of the function is (-∞, +∞)
Range of the function is [-1, +∞).
Step-by-step explanation:
The function has a graph in two parts.
The right side part passes through the points (-2,-1) and (0,3).
So, the equation of this part will be
[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - 0}{0 - (- 2)}[/tex]
⇒ y - 3 = 2x
⇒ y = 2x + 3
Again, the left side part of the graph passes through the points (-2,-1) and (-4,3).
Therefore, the equation of this part will be
[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - (- 4)}{- 4 - (- 2)}[/tex]
⇒ y - 3 = - 2(x + 4)
⇒ y - 3 = - 2x - 8
⇒ y = - 2x - 5
Therefore, the function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2. (Answer)
The vertex of the function is (-2,-1) (Answer)
Domain of the function is (-∞, +∞) (Answer)
Range of the function is [-1, +∞). (Answer)
