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:
[tex]f(x) = 4\left(\frac{2}{5}\right)^{x + 3} - 4[/tex]
Hence:
[tex]\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[/tex]
[tex]\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[/tex]
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 https://brainly.com/question/22026723
#SPJ1
