What is the range of the function f(x) = −(x + 3)2 + 7?

(-∞,7]

Step-by-step explanation:

This parabola is negative. This means that the vertex will be the highest possible y value. The vertex of this parabola is at (-3,7). This means that the range would be (-∞,7]

y ≤ 7

               Interval notation is: (-∞, 7]

Step-by-step explanation:

First, remember that range represents the y-values of the function.

-(x + 3)² + 7  is in vertex form: a(x - h)² + k   where

Therefore, the parabola has a maximum y-value at k (which is 7) and continues downward to negative infinity.  ⇒ Range: y ≤ 7

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

is there a question here?

step-by-step explanation: