Question

The function f(x) = –x2 – 4x + 5 is shown on the graph. Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.

Answer 1

we have

$f(x) = -x^{2} - 4x + 5$

using a graph tool

see the attached figure

the domain of the function is all real numbers------> the interval is (-∞,∞)

the range of the function is --------------------------------> the interval (-∞,9]

therefore

the answer is

The range of the function is all real numbers less than or equal to $9$

Answer 2

The range of the function is all real numbers greater than or equal to 9.
proof

f’= -2x-4=0

-2x=4  and x=4/-2=-2

F(-2)=-4 +8+5=9

F has a minimum point at (-2, y=9)

So 

The range of the function is all real numbers y>=9