The graph of an exponential function has a negative y-intercept and a common ratio ( r) such that 0< r<1. Which statements below are true? Select all that apply.

Question

As x increases, y decreases.

As x decreases, y decreases.

As x increases, y approaches 0.

As x decreases, y approaches 0.

The function is a decreasing function.

The function is an increasing function.

Answer 1

As x increases, y decreases.

As x decreases, y approaches 0.

The function is a decreasing function.

Answer 2

The function f(x)=735(1/2)^x models the number of grams in a sample of a radioactive substance after x years. Which statements are true about the sample? Select all that apply.

A. The sample is growing.

B. The sample is decaying.

C. The sample grows to 5,880 after 3 years.

D. The initial amount of the sample is 735 grams.

E. The sample decays to 91.875 grams after 3 years.

Answer 3

B. The sample is decaying.

D. The initial amount of the sample is 735 grams.

E. The sample decays to 91.875 grams after 3 years.

Answer 4

The function f(x)=3^x−3 is an exponential function containing the points (0, -2) and (2, 6).

The function g(x)=−1/2f(x)+3 contains points

A. (0, 2)

B. (0, 4)

C. (-2, 3)

D. (-2, 2)

Answer 5

The function f(x) = 3^x - 3 contains the points (0, -2) and (2, 6).

When given the generic form -1/2f(x)+3, we need to find the corresponding points for g(x).

For the point (0, -2):
g(0) = -1/2f(0) + 3
g(0) = -1/2(-2) + 3
g(0) = 1 + 3
g(0) = 4

Therefore, the point (0, 4) is contained in the function g(x).

For the point (2, 6):
g(2) = -1/2f(2) + 3
g(2) = -1/2(6) + 3
g(2) = -3 + 3
g(2) = 0

Therefore, the point (2, 0) is contained in the function g(x).

Therefore, the correct answers are:

B. (0, 4)

A. (0, 2)