Answer:
![\large\boxed{f(x)=\dfrac{4}{x+2}+5}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bf%28x%29%3D%5Cdfrac%7B4%7D%7Bx%2B2%7D%2B5%7D)
Step-by-step explanation:
![f(x)=\dfrac{a}{x-b}+c\\\\\text{We have}\\\text{(1) the vertical asymptote}\ x=-2.\ \text{Therefore}\ b=-2.\\\text{(2) the horizontal asymptote}\ y=5.\ \text{Therefore}\ c=5.\\\text{(3) the point (0, 7). Put the coordinates of the point to the equation}\\\text{of the function}\\y=\dfrac{a}{x-(-2)}+5\\\\7=\dfrac{a}{0+2}+5\qquad\text{subtract 5 from both sides}\\\\2=\dfrac{a}{2}\qquad\text{multiply both sides by 2}\\\\4=a\to a=4\\\\\text{Finally:}\\\\f(x)=\dfrac{4}{x+2}+5](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Ba%7D%7Bx-b%7D%2Bc%5C%5C%5C%5C%5Ctext%7BWe%20have%7D%5C%5C%5Ctext%7B%281%29%20the%20vertical%20asymptote%7D%5C%20x%3D-2.%5C%20%5Ctext%7BTherefore%7D%5C%20b%3D-2.%5C%5C%5Ctext%7B%282%29%20the%20horizontal%20asymptote%7D%5C%20y%3D5.%5C%20%5Ctext%7BTherefore%7D%5C%20c%3D5.%5C%5C%5Ctext%7B%283%29%20the%20point%20%280%2C%207%29.%20Put%20the%20coordinates%20of%20the%20point%20to%20the%20equation%7D%5C%5C%5Ctext%7Bof%20the%20function%7D%5C%5Cy%3D%5Cdfrac%7Ba%7D%7Bx-%28-2%29%7D%2B5%5C%5C%5C%5C7%3D%5Cdfrac%7Ba%7D%7B0%2B2%7D%2B5%5Cqquad%5Ctext%7Bsubtract%205%20from%20both%20sides%7D%5C%5C%5C%5C2%3D%5Cdfrac%7Ba%7D%7B2%7D%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%202%7D%5C%5C%5C%5C4%3Da%5Cto%20a%3D4%5C%5C%5C%5C%5Ctext%7BFinally%3A%7D%5C%5C%5C%5Cf%28x%29%3D%5Cdfrac%7B4%7D%7Bx%2B2%7D%2B5)
Hi there!
Unfortunately, the set of ordered pairs does NOT represent a function! This is because there are two of the same x values. In a function, there is one input for every output. In this case, there are two of the same inputs. However, there can be two of the same outputs.
Just to clarify - Not a function
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Answer:
Well the cases ... lets seee the cases show well I CAN NOT SEE THE CASES
Step-by-step explanation:
Answer:
x=-7
Step-by-step explanation:
add 4 to both sides. leaving you with x=-7
Remplace the values!!!
((5)2-1) divided 6
9 divided 6
3/2 or 1,5