# why might function notation be important? the reasons notation is used?

Once you get out of three dimensional functions, it is hard to write it any other way. Example:

f(x,y,z,t, u, v)=2x +y*e^{t} + uv -3zuv^{2}

## to rent a dvd a customer must pay $3.99 plus $0.99 for every day that it is late, write a rule in function notation for this situation?

f(x)=3.99+0.99x

## Function notation is important for several reasons. Here are a few:

1. Simplification: Function notation allows us to represent complex mathematical relationships concisely. Instead of writing out the entire equation every time we wish to refer to it, we can simply use the function notation. This saves time, space, and makes mathematical communication more efficient.

2. Clarity: Function notation can provide clarity by specifying the input and output variables explicitly. For example, in the function notation f(x, y, z, t, u, v) = 2x + y*e^t + uv - 3zuv^2, it is clear that the variables x, y, z, t, u, and v are inputs to the function, and the expression on the right-hand side represents the output.

3. Generalization: Function notation allows us to generalize mathematical relationships. By representing a relationship as a function, we can study the properties and behaviors of the relationship as a whole, rather than focusing on specific instances. This helps in understanding and analyzing patterns and trends.

4. Computation: Function notation enables us to perform mathematical operations with functions. We can evaluate functions at specific values or manipulate them algebraically. This is particularly useful when working with complex functions, as in the example you provided.

To evaluate the function at specific values, simply substitute the given values into the function expression. For example, if you want to find the value of the function f at x = 3, y = 2, z = 1, t = 0, u = -1, and v = 4, substitute these values into the function expression:

f(3, 2, 1, 0, -1, 4) = 2(3) + 2*e^0 + (-1)(4) - 3(1)(-1)(4)^2

Evaluate each term according to the order of operations (parentheses, exponents, multiplication, addition, subtraction) to find the result.

By using function notation and following the appropriate steps, we can better understand and work with complex mathematical relationships.