# High School Math : Understanding Functional Notations

## Example Questions

### Example Question #1 : Understanding Functional Notations

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

Horizontal line test

Calculating zeroes

Vertical line test

Calculating domain and range

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 #1 : Understanding Functional Notations

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.

### Example Question #3 : Understanding Functional Notations

If  and , what is ?

Explanation:

means gets plugged into .

Thus .

### Example Question #4 : Understanding Functional Notations

Let and .  What is ?

Explanation:

Calculate and plug it into .

### Example Question #1 : Understanding Functional Notations

Evaluate  if and .

Undefined