Question

What statements are true about the function f(x) = -1x^2 - 2? Check all that apply.

The parent function and this function open in the same direction.
The parent function and this function have the same range.
The parent function and this function have the same domain.
The range of the function is all real numbers less than or equal to -2.
The domain of the function is all real numbers greater than or equal to -2.
There are no values from the domain of the parent function that are also in the domain of this function.

Answer 1

The parent function and this function open in the same direction, and they have the same domain. However, they do not have the same range, and there are values from the domain of the parent function that are also in the domain of this function.

Step-by-step explanation:

The function f(x) = -1x^2 - 2 is a quadratic function with a negative leading coefficient, which means the parabola opens downwards. So, the parent function and this function open in the same direction. However, the range of the parent function is all real numbers less than or equal to 0, while the range of this function is all real numbers less than or equal to -2. Therefore, the statement 'The parent function and this function have the same range' is not true. The domain of the parent function is all real numbers, while the domain of this function is also all real numbers.

So, the statement 'The parent function and this function have the same domain' is true. Lastly, since the function is defined for all real numbers, there are values from the domain of the parent function that are also in the domain of this function. Therefore, the statement 'There are no values from the domain of the parent function that are also in the domain of this function' is not true.