Describe the end behavior of g(x) = e^-2x.

Question

Accepted Answer

Welcome back, everyone. In this problem, which of the following statements describes the end behavior of H X equals E-6X? A says the function approaches 6 as x approaches infinity and increases without bound as x approaches negative infinity. B says the function approach is zero as X approaches infinity and increases without bound as X approaches negative infinity. C says the function decreases without bound as x approaches infinity and increases without bound as x approaches negative infinity. And D says the function increases without bond as X approaches infinity and approaches 0 as X approaches negative infinity. Now if we're going to choose which statement best describes the end behavior of H of X, then we'll need to understand how our function H of X behaves at the ends. In other words, what does it do as it approaches infinity and negative infinity? That is, as X sorry, approaches infinity and negative infinity. Well, notice that H of X is an exponential function. What do we know about the general end behavior of exponential functions? Well, recall, OK, that for an exponential function F X equals E K X, OK. Then if K, the coefficient of X is positive, OK, then, The function approach is 0 as x approaches negative infinity and increases without bound as x approaches infinity. In other words, we could say that the limit of F of X as X approaches infinity is equal to infinity. It increases without bound, while the limit. Of F of X as X approaches negative infinity equals 0. Now, what if K is less than 0? Well, we also know that if K is less than 0, OK, then the function. Approaches 0 as x approaches infinity. OK. In other words, as X approaches infinity, F of X approaches 0, while it increases with bound as x approaches negative infinity. In other words, the limit as X approaches negative infinity. Of F of X is equal to infinity. So with that in mind, how can that help us to find the end behavior of HFX? Well, let's apply that knowledge to this function, OK? Since HF X. Is equal to -6X comparing it to the general form of an exponential function, K is equal to -6 and 6 is less than 0. So since K is less than 0, we can conclude it takes on the behavior as specified here in our diagram in in what we discussed before for a general form. In other words, H X approaches 0 as X approaches infinity and increases without bound as X approaches negative infinity. Therefore, B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Describe the end behavior of g(x) = e^-2x.

Key Concepts

End Behavior of Functions

Exponential Functions

Limits at Infinity

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Describe the end behavior of g(x) = e-2x.

Key Concepts

End Behavior of Functions

Exponential Functions

Limits at Infinity

Watch next

Describe the end behavior of g(x) = e^-2x.