Question

The function f(x) = −(x + 5)(x + 1) is shown. 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

Answer 1

all real numbers such that y is less than or equal to 4

Answer 2

all real numbers less than or equal to 4.

Step-by-step explanation

The given function is

`f(x) = - (x + 5)(x + 1)`

Expand

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

`f(x) = - ( {x}^(2) + 6x + 5)`

`f(x) = - {x}^(2) - 6x - 5`

a=-1,b=-6,c=-5

The x-value of the vertex is given by

a=-1,b=-6,c=-5

`x = ( - b)/(2a)`

`x = - ( - 6)/(2( - 1)) = - 3`

The y-value of the vertex is

`f( - 3) = - ( - 3 + 5)( - 3 + 1)`

`f( - 3) = - ( 2)( - 2) = 4`

Since a=-1, the function opens downwards.

The highest value is the y-value of the vertex which is 4.

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

The correct choice is A.