 Functions and Equations MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts Let's take a look at some equations, using two variables,
which can be used to express functions.

Functions such as:    y = 3x + 10 (linear)    or    y = x2 + 4 (non-linear)

The two variables are x and y, where x is the independent variable.
Functions represent the "relationships between variables".

 Things to keep in mind: • Not ALL equations are functions (consider x + 2 = 8 : it has only 1 variable) • Not ALL functions are represented as equations (some functions are represented in a table or as a graphical display). 1 Given the equation 2x + y = 15. Write the equation in "y =" form. Solution: We need to solve this equation for y, so that an expression with x remains. 2x + y = 15 y = -2x + 15 In "y =" form we have y = -2x + 15. 2 Given a function represented by the equation ½ y + ¾ x = 4. Write the equation equation in "y =" form. Solution: We need to solve this equation for y, so that an expression with x remains. ½ y + ¾ x = 4 ½ y = 4 - ¾ x y = 8 - 1½ x In "y =" form we have y = 8 - 1½ x. 3 Given an input value of x, the function outputs a value y to satisfy the equation 2y + 4x = 82. Write the equation in "y =" form. Solution: Solve the equation for y, so that an expression with x remains. 2y + 4x = 82 2y = -4x + 82 y = -2x + 41 In "y =" form we have y = -2x + 41. In plain English ... ... equations for functions are generally expressed in "y =" form. Most graphing calculators graph only functions, where the equation is entered in a "y =" location on the calculator. NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use".