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.
<h3>What is the end behavior of a function f(x)?</h3>
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](https://tex.z-dn.net/?f=f%28x%29%20%3D%204%5Cleft%28%5Cfrac%7B2%7D%7B5%7D%5Cright%29%5E%7Bx%20%2B%203%7D%20-%204)
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](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%20-%5Cinfty%7D%20f%28x%29%20%3D%20%5Clim_%7Bx%20%5Crightarrow%20-%5Cinfty%7D%204%5Cleft%28%5Cfrac%7B2%7D%7B5%7D%5Cright%29%5E%7Bx%20%2B%203%7D%20-%204%20%3D%204%5Cleft%28%5Cfrac%7B5%7D%7B2%7D%5Cright%29%5E%7B%5Cinfty%20%2B%203%7D%20-%204%20%3D%20%5Cinfty%20-%204%20%3D%20%5Cinfty)
![\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](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%20%5Cinfty%7D%20f%28x%29%20%3D%20%5Clim_%7Bx%20%5Crightarrow%20-%5Cinfty%7D%204%5Cleft%28%5Cfrac%7B2%7D%7B5%7D%5Cright%29%5E%7Bx%20%2B%203%7D%20-%204%20%3D%204%5Cleft%28%5Cfrac%7B2%7D%7B5%7D%5Cright%29%5E%7B%5Cinfty%20%2B%203%7D%20-%204%20%3D%200%20-%204%20%3D%20-4)
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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Answer:
f(g(x))=9-x-![x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D)
Step-by-step explanation:
Given ,
f(x)=9-x
g(x)=
+x
here,.
fog
=f(g(x))
=f(
+x)
=9-(
+x)
=9-
-x
=9-x-![x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D)
Answer:
1.2
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
have a nice day
Answer:
1. y=-5x+5
2. y=3x
3. the slope is 6 and the y-intercept is 7
Step-by-step explanation: