# Math

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in September 2020. This work is licensed under a Creative Commons BY 4.0 International License .

Functions

### Domain and Range of a Function:

##### Linear Functions: A general linear function has the form f(x)=ax+b, where a and b are constant numbers. Since there are no restrictions on the possible values for x, the domain of a linear function is all real numbers. We use the following notations to represent the domain:

##### where a, b, and c are constants. A quadratic function is defined for all real numbers, therefore the domain is

##### as you see, the square root function is defined for zero or positive x values. So, the domain of the function is given by:

##### Trigonometric Functions: The domain of the sine and cosine functions are all real numbers, therefore:

##### In order to find the domain of f, one has to check for all restrictions on the function. We have a square root in the denominator which can only  have positive numbers or zero as the input. However, since we can not have zero in the denominator, we have the following restriction on the function:

##### solving the above restriction gives the domain of the function

##### In order to find the domain of f, we use the following trig identity