Question

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

3. For some x-values, the y-value of the exponential function is smaller.

4. For some x-values, the y-value of the exponential function is greater.

5. For any x-value greater than 7, the y-value of the exponential function is greater.

Explanation:

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Answer 2

3. For some x-values, the y-value of the exponential function is smaller.

4. For some x-values, the y-value of the exponential function is greater.

5. For any x-value greater than 7, the y-value of the exponential function is greater.

Explanation:

We are given the functions,

`y=2x^2\\\\y=2^x`

It is required to find the true statements of the functions.

From the graphs of the functions below, we have that the graphs intersect at the point (6.32,79.878).

To the left of the point, we have that the exponential function have smaller y-values than the parabola.

To the right of the point, we have that the exponential function have greater y-values than the parabola.

Moreover, after x= 7, the y-values of the exponential function are always greater than parabola.

Thus, the correct options are 3, 4 and 5.