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

(-∞, 4)

Step-by-step explanation:

"The function f(x)= -(x+5)(x+1) is down" should be "The function f(x)= -(x+5)(x+1) has a parabolic graph that opens down."

Expanding f(x)= -(x+5)(x+1), we get  f(x) = -[x^2 + 6x + 5] = -x^2 - 6x - 5.

Here the coefficients are a = -1, b = -6 and c = -5.  Thus, the axis of symmetry is

         -(-6)

x = = -3.  

        2(-1)

The maximum value of the function occurs  when x = -3.

We must also find the actual max value.  

It is f(-3) = -(-3)^2 - 6(-3) - 5, or 4.

The max value is 4.  Thus, the range of this function is (-∞, 4)

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step-by-step explanation:

x= -3

step-by-step explanation:

step 1: simplify brackets

4 - x - 1 = 6

step 2: simpilfy

3 - x = 6

step 3: subtract 3 from both sides

-x = 6 - 3

step 4: simpilfy 6 - 3

-x = 3

step 5: multiply both sides by -1

x = -3