Question

What is the end behavior of the graph of the exponential function f(x)=b x when 0

A) Asymptotically approaches 0 as x approaches infinity
B) Asymptotically approaches 0 as x approaches negative infinity
C) Approaches positive infinity as x approaches infinity
D) Approaches positive infinity as x approaches negative infinity

Answer 1

The end behavior of the exponential function f(x) = bx depends on the value of b. If b is greater than 1, the function approaches positive infinity as x approaches positive infinity. If b is between 0 and 1, the function approaches 0 as x approaches positive infinity.

Step-by-step explanation:

The end behavior of the graph of the exponential function f(x) = bx depends on the value of b.

If b is greater than 1, then as x approaches positive infinity, f(x) also approaches positive infinity (Option C). This is because the function grows exponentially as x increases.

If b is between 0 and 1, then as x approaches positive infinity, f(x) approaches 0 (Option A). This is because the function exponentially decreases as x increases.

In both cases, the function does not have any asymptotes or limits as x approaches infinity (Options A and C). Therefore, the correct answers are Options A and C.