Use this graph of F(x) to decide which of the statements below are true.

Question

A. the number 2 is in the range of F(x)

B. The range of F(x) is -1<y>1

C. y = x^2 - 6x - 15

D. All numbers are in the domain of F(x)

Answer 1

Option A is correct.

Answer 2

The Graph represents a polynomial F(x).

Observe the graph, the x - intercepts are - 1, 0, 1.

Therefore, the polynomial is like this : F(x) = a(x + 1)(x - 0)(x - 1).

This polynomial is passing through the point : (- 1/2, 1/2).

Therefore, the polynomial is F(- 1/2) = a(- 1/2 + 1)(- 1/2  - 0)(- 1/2 - 1) = 1/2.

a(- 1/2 + 1)(- 1/2  - 0)(- 1/2 - 1) = 1/2

a(1/2)(- 1/2)(- 3/2) = 1/2

3a/8 = 1/2

3a = 4

a = 4/3.

Therefore, the polynomial is (4/3)(x + 1)x(x - 1).

The domain of the polynomial :

(4/3)(x + 1)x(x - 1) 0

x - 1, x 0, and x 1.

Therefore, domain of the polynomial is all real numbers except - 1, 0, and  1.

range of the polynomial :

range  : - 1/2  ≤ y ≥ 1/2.

So, the number 2 is in the range of F(x).

Option A is the correct choice.