Functional Notation

1.0 Basic functional notation can be written in the form:

• y = f(x), which reads y is a function of the variable x.
• s = h(t), s is a function of the variable t,
• q = m(u), q is a function of the variable u.

2.0 If we know the exact nature of the functional relationship we can write it. For example it could be written as follows:

• y = f(x) = 2x² + 14x - 3
• s = h(t) = 16t² + 30t
• q = m(u) = 0.5u - 2

Note: I have just made up these relationships to illustrate the point.

3.0 When you are asked to evaluate a function at some point it could look like:

• Example 1
• y = f(x) = 2x² + 14x - 3
• Let x = 3
• y = f(3) = 2(3)² + 14(3) - 3
• You have replaced the variable x with its value which in this case is 3.
• y = f(3) = 2(9) + 42 - 3 = 18 + 42 - 3 = 57 This is the final answer.
• -------------------
• Example 2
• s = h(t) = 16t² + 20t
• Let t = 2v
• s = h(2v) = 16(2v)² + 20(2v) = 64v² + 40v
• In this case you have replaced t with its value which happens to be 2v (it doesn’t have to be a number).
• -------------------
• Example 3
• q = m(u) = 0.5u - 2
• Let u = g-1
• q = m(g-1) = 0.5(g-1) -2 You have replaced u with its value of g-1.

  q = m(g-1) = 0.5g - 0.5 - 2 = 0.5g - 2.5 This is the final answer.

Practice in the calculation of function values

The material that follows is designed to let you calculate the value of a function for various values of x. Specifically the tool shown below will calculate the value of the following functions:

1. Natural logarithm, ln(a*x - b), you will enter; ln, and values for x, a and b
2. Common logarithm, log(a*x - b), you will enter: log, and values for x, a and b
3. Absolute value, |a*x - b|, you will enter: abs, and values for x, a and b
4. Power function, a*x^b, you will enter: pow, and values for x, a and b
5. Exponential function, a*b^x, you will enter: exp, and values for x, a and b
6. Square root, Sqrt(a*x - b). you will enter: sqrt, and values for x, a and b
7. DO NOT CAPITALIZE ANY OF THE ALPHABETIC ENTRIES, CASE SENSITIVE!

You enter the name of the function and the value of the variable x and the constants a and b. If your inputs are feasible you will get an answer. If they are not possible you will get an answer of Nan, or -Infinity or + Infinity depending on the browser you are using and a host of other factors. If you don't get numbers your inputs are probably not within the domain of the function. The bottom box allows you to write the answer you expect to get. You could estimate it or calculate it with your calculator. Then use the tool to calculate the same answer and see if they agree. If you have any problems with the tool let me know.