Question

The function f(x) = -(x + 5)(x+1) What is the range of the function?

all real numbers less than or equal to 4
all real numbers less than or equal to -3
all real numbers greater than or equal to 4
all real numbers greater than or equal to -3
-410-X

Answer 1

All real numbers less than or equal to 4.

Explanation:

Rearrange it to vertex form:

-(x + 5)(x+1)

= - (x^2 + 6x + 5)

= - [( x + 3)^2 - 9 + 5]

= - (x + 3)*2 + 4

So the vertex is at f(x) = 4 and its a maximum because the coefficient of x^2 is negative.

So the range is all real numbers less than or equal to 4.