Module 4, Lesson 4 Online Algebra VHS@PWCS Function Families Module 4, Lesson 4 Online Algebra VHS@PWCS

In this lesson, we are going to look at 3 different function families. In your studies of mathematics you will look time and time again and similarities and differences and at different functions. In this lesson, we are going to look at 3 different function families. Linear Functions Quadratic Functions Absolute Value Functions We will study linear and quadratic functions in depth and just introduce absolute value functions.

Linear Functions Linear functions are functions whose graph is a straight line. The colored lines to the left are each linear functions. The standard form of an equation of a linear function is: ax +by = c

Linear Functions The standard form of an equation of a linear function is: ax +by = c a and b cannot be zero Examples of linear functions are: 3x – 4y = -3 x + y = 0 -2x + y = 7 Notice that in each of these equations There are no exponents There are 2 variables in this case x and y. Keeping the above in mind other examples of linear functions are: y = -3x y = 5x – 8

Quadratic Functions Quadratic function graphs are “u”shaped. We call this shape/graph a parabola. The colored graphs to the right are quadratic functions/parabolas. The standard form of a quadratic function is: ax2 + bx + c = y

Quadratic Functions The standard form of a quadratic function is: ax2 + bx + c = y Examples of equations of quadratic functions are: y = 5x2 + 3x + 1 y = x2 -9 y = -2x2 Notice that in these equations: Again there is 2 variables, x and y There is always a term that is squared or taken to the second power.

Absolute Value Functions The graphs of absolute value functions are “V” shaped. The colored lines to the left are graphs of absolute value functions. The standard form of an equation of an absolute value function is: y = | ax + b |

Absolute value functions The standard form of an equation of an absolute value function is: y = | ax + b | Examples of absolute value equations are: y = 2| x | y = | x – 3 | y = 3| 2x + 4| - 4 Notice that in these examples: There are again 2 variables, x and y. That in all equations there is some quantity in the absolute value symbols ( | | )

Review In this lesson all I want you to be able to do is recognize what type of function each equation or graph is. Linear functions Graphs are a straight line Equations have 2 variables and no term taken to a power. Quadratic functions Graphs are “U” shaped, parabolas Equations have 1 term take to the second power Absolute Value functions Graphs are “V” shaped Equations have the some quantity in absolute value symbols.