Question

the function $f(x) = -x^2 - 4x + 5$ is shown on the graph.
which statement about the function is true?
○ the domain of the function is all real numbers less than or equal to -2.
○ the domain of the function is all real numbers less than or equal to 9.
○ the range of the function is all real numbers less than or equal to -2.
○ the range of the function is all real numbers less than or equal to 9.

Explanation:

Step1: Analyze domain of quadratic

For any quadratic function $f(x)=ax^2+bx+c$, the domain is all real numbers, since there are no restrictions on $x$-values that make the function undefined.

Step2: Analyze range of quadratic

This is a downward-opening parabola ($a=-1<0$), so it has a maximum value at its vertex. The vertex is given as $(-2,9)$, so the highest $y$-value is 9, and all other $y$-values are less than or equal to 9.

Answer:

The range of the function is all real numbers less than or equal to 9.