Question



The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?

The domain is all real numbers. The range is y < 16.

The domain is all real numbers. The range is y ≤ 16.

The domain is {x|–5 < x < The range is y < 16.

The domain is {x|–5 ≤ x ≤ The range is y.

Answer 1

it is the 2nd one if im not right then idk

Answer 2

Answer with explanation:

⇒Domain:

f(x)= -x² -2 x +15

= - (x²+2 x -15)

Splitting the middle term

= - (x²+5 x - 3 x -15)

= -[ x × (x+5) -3× (x+5)]

= -(x-3)(x+5)

y=f(x)=(3 -x)(x+5)

Domain of the function is defined as set of all values of x, for which y is defined.

f(x) is defined as all real values of x.So, Domain = R.

⇒Range:

`y=-x^2-2 x +15\\\\y=-(x^2+2 x-15)\\\\ y=-[(x+1)^2-1-15]\\\\y= -(x+1)^2+16\\\\ 16 -y=(x+1)^2\\\\x+1=\pm√(16-y)\\\\x=\pm√(16-y)-1`

Range of the function is defined as set of all values of y, for which x is defined.

⇒16 -y ≥ 0

⇒y ≤ 16

Option B

The domain is all real numbers. The range is y.