Question

Compare the functions y = 2x² and y = 2x. Which of the following statements are true? Check all that

apply.
O For any x-value, the y-value of the exponential function is always greater.
For any x-value, the y-value of the exponential function is always smaller.
For some x-values, the y-value of the exponential function is smaller.
For some x-values, the y-value of the exponential function is greater.
For any x-value greater than 7, the y-value of the exponential function is greater.
For equal intervals, the y-values of both functions have a common ratio.

Answer 1

When comparing the functions y = 2x² and y = 2x, several statements are true: the y-value of the exponential function is always greater for any x-value; the y-value of the exponential function is smaller for some x-values, such as negative x-values; and the y-value of the exponential function is greater for any x-value greater than 7.

Step-by-step explanation:

When comparing the functions y = 2x² and y = 2x, several statements are true:

• For any x-value, the y-value of the exponential function is always greater. This is true because as x increases, x² grows faster than x, resulting in a greater y-value.
• For some x-values, the y-value of the exponential function is smaller. This is true for negative x-values, where x² is smaller than x.
• For any x-value greater than 7, the y-value of the exponential function is greater. This is true because for x > 7, 2x² will always be greater than 2x.

Learn more about Comparison of exponential and linear functions