Answer:
![f(x)=2x+10](https://tex.z-dn.net/?f=f%28x%29%3D2x%2B10)
Step-by-step explanation:
The given tables shows a relation that can be transform into a function.
From the table we deduct that each toppings cost $2, because for 1 topping is $12, for 2 is $14, for 3 is $16, and so on. So, the ratio of change is
![m=\frac{\Delta y}{\Delta x}=\frac{2}{1}=2](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%3D%5Cfrac%7B2%7D%7B1%7D%3D2)
Where
represents the cost and
represents the number of toppings.
Now, we use one pair from the graph (1,12), the ratio of change and the point-slope formula to find the function
![y-y_{1}=m(x-x_{1})\\y-12=2(x-1)\\y=2x-2+12\\y=2x+10](https://tex.z-dn.net/?f=y-y_%7B1%7D%3Dm%28x-x_%7B1%7D%29%5C%5Cy-12%3D2%28x-1%29%5C%5Cy%3D2x-2%2B12%5C%5Cy%3D2x%2B10)
Therefore, the function that expresses the given situation is
![f(x)=2x+10](https://tex.z-dn.net/?f=f%28x%29%3D2x%2B10)
Where ![y=f(x)](https://tex.z-dn.net/?f=y%3Df%28x%29)