The function given is F(x) = 4 * 5^x.

A. The y-intercept is (0, 5).
This is not true. The y-intercept of a function is the point where the graph of the function intersects the y-axis. This happens when x = 0. Substituting x = 0 into the function gives F(0) = 4 * 5^0 = 4. So, the y-intercept is (0, 4), not (0, 5).

B. It is decreasing.
This is not true. The function F(x) = 4 * 5^x is an exponential function where the base (5) is greater than 1. This means the function is increasing, not decreasing.

C. The range of F(x) is y 5.
This is not true. The range of an exponential function of the form F(x) = a * b^x (where a 0 and b 1) is y 0. In this case, since a = 4, the range of F(x) is y 4, not y 5.

D. The y-intercept is (0, 4).
This is true. As explained in point A, the y-intercept of the function is (0, 4).

E. The domain of F(x) is all real numbers.
This is true. The domain of an exponential function is all real numbers.

F. It is increasing.
This is true. As explained in point B, the function is increasing because the base of the exponential (5) is greater than 1.

So, the true facts for the graph of the function F(x) = 4 * 5^x are D, E, and F.

Question

The function given is F(x) = 4 * 5^x.

A. The y-intercept is (0, 5).
This is not true. The y-intercept of a function is the point where the graph of the function intersects the y-axis. This happens when x = 0. Substituting x = 0 into the function gives F(0) = 4 * 5^0 = 4. So, the y-intercept is (0, 4), not (0, 5).

B. It is decreasing.
This is not true. The function F(x) = 4 * 5^x is an exponential function where the base (5) is greater than 1. This means the function is increasing, not decreasing.

C. The range of F(x) is y > 5.
This is not true. The range of an exponential function of the form F(x) = a * b^x (where a > 0 and b > 1) is y > 0. In this case, since a = 4, the range of F(x) is y > 4, not y > 5.

D. The y-intercept is (0, 4).
This is true. As explained in point A, the y-intercept of the function is (0, 4).

E. The domain of F(x) is all real numbers.
This is true. The domain of an exponential function is all real numbers.

F. It is increasing.
This is true. As explained in point B, the function is increasing because the base of the exponential (5) is greater than 1.

So, the true facts for the graph of the function F(x) = 4 * 5^x are D, E, and F.

Knowee AI · Accepted Answer

The function given is F(x) = 4 * 5^x.

A. The y-intercept is (0, 5).
This is not true. The y-intercept of a function is the point where the graph of the function intersects the y-axis. This happens when x = 0. Substituting x = 0 into the function gives F(0) = 4 * 5^0 = 4. So, the y-intercept is (0, 4), not (0, 5).

B. It is decreasing.
This is not true. The function F(x) = 4 * 5^x is an exponential function where the base (5) is greater than 1. This means the function is increasing, not decreasing.

C. The range of F(x) is y > 5.
This is not true. The range of an exponential function of the form F(x) = a * b^x (where a > 0 and b > 1) is y > 0. In this case, since a = 4, the range of F(x) is y > 4, not y > 5.

D. The y-intercept is (0, 4).
This is true. As explained in point A, the y-intercept of the function is (0, 4).

E. The domain of F(x) is all real numbers.
This is true. The domain of an exponential function is all real numbers.

F. It is increasing.
This is true. As explained in point B, the function is increasing because the base of the exponential (5) is greater than 1.

So, the true facts for the graph of the function F(x) = 4 * 5^x are D, E, and F.

Which facts are true for the graph of the function below? Check all that apply.F(x) = 4∙∙ 5xA.The y-intercept is (0, 5).B.It is decreasing.C.The range of F(x) is y > 5.D.The y-intercept is (0, 4).E.The domain of F(x) is all real numbers.F.It is increasing.SUBMITarrow_backPREVIOUS

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