1 1 Functions and Models 1 2 Graphs f Functions 1 3 Linear Functions 1 4 Equations of Lines 2 1 Algebraic Graphical Solutions of Linear Functions 2 2 Fitting Lines to Data Points Modeling Linear Functions 3 1 Quadratic Functions and Parabolas 3 2 Solving Quadratic Equations 3 3 Power Functions Piecewise Defined Functions sometimes a single form cannot describe the whole situation We can use a Piecewise Defined Functions in this case You can treat them as a single formula even if they are very irregular Example 49 0 x 1 70 1 x 2 91 2 x 3 112 3 x 3 5 Example 2 f x 5 x 2 Example 3 Specific Heat Capacity heat necessary to raise the temperature by 1 degree C where heat is the energy used Latent Heat Heat necessary to liquefy ice temperature raised vs Heat Absolute Value Function f x x x 0 x Absolute f x x Remark x represents true distance od the point representing x to the original Added point on the real axis Example Solving Absolute Value Equations equations that contain absolute value symbols 1 If x a a 0 x a OR x a 2 If x 0 x 0 3 There is no solution to x a if a 0 because an absolute value cannot be negative Example Solve Example 2 x 3 9 1 9 0 so x 3 9 OR x 3 9 2 x 6 OR x 12 2 x 4 8 1 Remove absolute value symbole 2 Solve both equations for X 2x 4 8 or 4 4 2x 12 2 2 X 6 2x 4 8 4 4 2x 4 2 2 X 2 Power Functions is a function of the form y ax b where a b are real s numbers and b is not equal to Y x 2 is a power function so is x 2x because y 2 x 1 Squaring function y x 2 Cubing function y x 3