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What is the range of the function f(x) = -(x + 3)2 + 7?
all real numbers less than or equal to 7
all real numbers greater than or equal to 7
all real numbers less than or equal to -3
all real numbers greater than or equal to -3

Respuesta :

Baelayyy

Answer:

It's A-all real numbers less than or equal to 7

Step-by-step explanation:

I just took the unit test and got a 100 on it!

The range of the function f(x) = -(x + 3)² + 7 is {y: y ∈ R, y ≤ 7}. So, option A is correct.

How to find the range of a function?

  • Consider the given function as  y = f(x)
  • Solve for x ( isolate x from the equation)
  • The domain of the obtained function is the range of the function f(x).

Finding the range:

Given that,

f(x) = -(x + 3)² + 7

⇒ y = -(x + 3)² + 7

⇒ (x + 3)² = 7 - y

⇒ (x + 3) = √(7 - y)

⇒ x = (√(7-y)) - 3

Thus, all the real values less than or equal to 7 for y define the function. So, the domain for the obtained function is {y: y ∈ R, y ≤ 7}.

Therefore, the range of the given function is {y: y ∈ R, y ≤ 7}.

Learn more about the range of a function here:

https://brainly.com/question/2264373

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