Question

Help asap What is the end behavior of the following graph

Answer 1

Using limits, it is found that the end behavior of the graph is given as follows:

It rises to the left, and stays constant at y = -4 to the right.

What is the end behavior of a function f(x)?

It is given by the limits of f(x) as x goes to infinity.

In this problem, the function is given by:

$f(x) = 4\left(\frac{2}{5}\right)^{x + 3} - 4$

Hence:

$\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 4\left(\frac{2}{5}\right)^{x + 3} - 4 = 4\left(\frac{5}{2}\right)^{\infty + 3} - 4 = \infty - 4 = \infty$

$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow -\infty} 4\left(\frac{2}{5}\right)^{x + 3} - 4 = 4\left(\frac{2}{5}\right)^{\infty + 3} - 4 = 0 - 4 = -4$

Hence:

It rises to the left, and stays constant at y = -4 to the right.

More can be learned about limits and end behavior at brainly.com/question/22026723

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