The true statement is:
"The range of the function is all real numbers less than or equal to 9."
<h3>
Which statements are true?</h3>
Here we have the quadratic function:
![f(x) = -x^2 - 4x + 5](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-x%5E2%20-%204x%20%2B%205)
And we want to see which of the given statements are true.
The first one is:
"The domain is al real numbers less than or equal to -2"
This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).
The second statement is:
" The domain of the function is all real numbers less than or equal to 9."
Also false
Third one:
" The range of the function is all real numbers less than or equal to −2"
The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.
In this case, the quadratic function is:
![f(x) = -x^2 - 4x + 5](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-x%5E2%20-%204x%20%2B%205)
So the vertex is at:
![x = 4/(2*-1) = -2\\](https://tex.z-dn.net/?f=x%20%3D%204%2F%282%2A-1%29%20%3D%20-2%5C%5C)
Then the y-value of the vertex is:
![f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9](https://tex.z-dn.net/?f=f%28-2%29%20%3D%20-%28-2%29%5E2%20-%204%2A%28-2%29%20%2B%205%20%3D%20-4%20%2B%208%20%2B%205%20%3D%209)
So the range is the set of all real numbers less than or equal to 9.
So the above statement is false, and the final one:
"The range of the function is all real numbers less than or equal to 9."
Is the true statement.
If you want to learn more about quadratic functions:
brainly.com/question/1214333
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