Question

01:37:49

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

On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 3, 4), and goes through (negative 1, 0).
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 less than or equal to 4

Explanation:

The leading coefficient is negative, so the vertex is a maximum. The y-value of the vertex (4) is the upper limit of the range.

The range is all real numbers less than or equal to 4. (first choice)

Answer 2

all real numbers less than or equal to 4

which agrees with the first answer option listed

Explanation:

The parabola opening down means that its two branches go on towards negative values with no limit. The maximum y-value that this parabola can reach is therefore the y-value of its vertex which is 4, given that the vertex coordinates are (3, 4).

Therefore, the Range of y-values can have any real number that is smaller than or equal to 4