# High School Math : Understanding Functional Notations

## Example Questions

### Example Question #1 : Functions And Graphs

Which analysis can be performed to determine if an equation is a function?

Calculating domain and range

Calculating zeroes

Vertical line test

Horizontal line test

Vertical line test

Explanation:

The vertical line test can be used to determine if an equation is a function. In order to be a function, there must only be one (or ) value for each value of . The vertical line test determines how many (or ) values are present for each value of . If a single vertical line passes through the graph of an equation more than once, it is not a function. If it passes through exactly once or not at all, then the equation is a function.

The horizontal line test can be used to determine if a function is one-to-one, that is, if only one value exists for each (or ) value. Calculating zeroes, domain, and range can be useful for graphing an equation, but they do not tell if it is a function.

Example of a function: Example of an equation that is not a function: ### Example Question #2 : Functions And Graphs

Let and . What is ?      Explanation:

THe notation is a composite function, which means we put the inside function g(x) into the outside function f(x). Essentially, we look at the original expression for f(x) and replace each x with the value of g(x).

The original expression for f(x) is . We will take each x and substitute in the value of g(x), which is 2x-1.   We will now distribute the -2 to the 2x - 1. We must FOIL the term, because   Now we collect like terms. Combine the terms with just an x. Combine constants. The answer is .

### Example Question #1 : Understanding Functional Notations

If and , what is ?      Explanation: means gets plugged into .

Thus .

### Example Question #2 : Understanding Functional Notations

Let and .  What is ?      Explanation:

Calculate and plug it into .  ### Example Question #3 : Function Notation

Evaluate if and .  Undefined   Explanation: This expression is the same as saying "take the answer of and plug it into ."

First, we need to find . We do this by plugging in for in .  Now we take this answer and plug it into . We can find the value of by replacing with .   