Question

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

Answer 1

we have

$f(x)=-(x+3)^{2}+7$

we know that

The function is a vertical parabola open downward

The vertex is the point $(-3,7)$

The vertex is a maximum

The range is the interval-----------> (-∞,7]

That means

All real numbers less than or equal to $7$

therefore

the answer is the option

All real numbers less than or equal to $7$

Answer 2

all real numbers less than or equal to 7