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

Explanation:

Step1: Analyze the squared term

For any real number $x$, $(x+3)^2 \geq 0$

Step2: Multiply by -1

Multiply the inequality by -1 (reverse inequality): $-(x+3)^2 \leq 0$

Step3: Add 7 to both sides

Add 7 to all parts: $-(x+3)^2 + 7 \leq 0 + 7$, so $f(x) \leq 7$

Answer:

all real numbers less than or equal to 7