Final answer:
The exponential function y=2x² can have y-values greater or smaller than 2 for some x-values, but not for all x-values. The constant function y=2 always has a y-value of 2, regardless of the x-value. There is no specific information about the x-values greater than 7 in the given functions. The functions y=2x² and y=2 do not have a common ratio for equal intervals.
Step-by-step explanation:
When comparing the functions y=2x² and y=2, it's important to understand their properties. The function y=2x² is a quadratic function, while y=2 is a constant function that always has the same value of 2.
For any x-value, the y-value of the exponential function y=2x² can vary and is not always greater or always smaller than the constant function y=2. So, the statements 'For any x-value, the y-value of the exponential function is always greater' and 'For any x-value, the y-value of the exponential function is always smaller' are both false.
However, for some specific x-values, the y-value of the exponential function y=2x² can be smaller or greater than 2. For example, when x=0, y=2x² is equal to 0, while y=2 is still equal to 2. Therefore, the statements 'For some x-values, the y-value of the exponential function is smaller' and 'For some x-values, the y-value of the exponential function is greater' are both true.
Lastly, the statement 'For any x-value greater than 7, the y-value of the exponential function is greater' cannot be determined based on the given functions, as there is no explicit restriction or range mentioned in the question.
Regarding the statement 'For equal intervals, the y-values of both functions have a common ratio,' it does not apply here because the constant function y=2 does not have intervals like the quadratic function y=2x².
Learn more about Comparison of quadratic and constant functions