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

ANSWER

all real numbers less than or equal to 4.

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

$x = \frac{ - b}{2a}$

$x = - \frac{ - 6}{2( - 1)} = - 3$

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.