Question

Are u smarter than an 8th grader!?!

Answer 1

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  

$\frac{y - 3}{3 - (- 1)} = \frac{x - 0}{0 - (- 2)}$

⇒ 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  

$\frac{y - 3}{3 - (- 1)} = \frac{x - (- 4)}{- 4 - (- 2)}$

⇒ 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)