Final answer:
- No, there are no limitations for the equation y = -x² - 2x . (Option B)
- Yes. The graph of the equation has y-axis symmetry. (Option A. Yes, it has y-axis symmetry)
Step-by-step explanation:
1) The equation given is y = -x² - 2x. To determine if there are any limitations on the inputs, we need to consider the nature of the equation.
In this case, since the equation is a quadratic function, there are no explicit limitations on the inputs. This means that any real number can be used as an input for x in the equation.
Therefore, the correct answer is B) No, there are no limitations.
2) To determine if the graph has any symmetry, we can analyze the equation.
In this case, the equation is y = -x² - 2x. We can rewrite this equation as y = -x(x + 2).
The presence of the term "x" in the equation indicates that the graph may have symmetry. In particular, when a function has symmetry with respect to the y-axis, it means that replacing x with -x in the equation results in an equivalent equation.
Let's test this by replacing x with -x in the equation:
y = -(-x)(-x + 2)
y = x(x + 2)
As we can see, the equation remains the same. This indicates that the graph of the equation has y-axis symmetry.
Therefore, the correct answer is A) Yes, it has y-axis symmetry
Your question is incomplete, but most probably the full question was:
Equation: y= -x²-2x
1) Are there any limitations on the inputs of the equation?
A) Yes, there are limitations
B) No, there are no limitations
C) It is not mentioned in the question
D) The question is unclear about limitations
2) Does the graph have any symmetry? If so, where?
A) Yes, it has y-axis symmetry
B) Yes, it has x-axis symmetry
C) No, it does not have symmetry
D) The question does not provide information about symmetry