Inverse Functions of lines/quadratics/and cubics~ edited by Tyler Zeng, Jefferson Lam, Peng Feng

Inverse Relation A relation that maps the output values of an original relation back to their original input values. The graph of an inverse relation is the reflection of the graph of the original relation, with y = x as the line of reflection.

Inverse Function A relation and its inverse relation whenever both relations are functions. Functions f and g are inverses of each other provided f(g(x))=x and g(f(x))=x

Equation of table 1 y = x + 3 x = y + 3 switch x and y x - 3= y minus 3 from both sides The inverse of y = x + 3 is y = x - 3, which is the equation of table 2. Inverse of linear equation

Inverse of the equation~ table y = x + 3 switch the x values to y. X Y X Y

Inverse of a line~ The line reflects over y = x.

Inverse of Quadratics Similar to the inverse of a linear equation. Here there's just a little extra step~ Example problem~ f(x) = x² - 4x + 3( Starting equation ) x = y² - 4y + 3( Switch x and y ) x - 3 = y² - 4y( Subtract 3 from both sides ) x = y² - 4y + 4 ( Complete square by adding 4 ) x + 1 = (y - 2)²( Simplify ) √x+1 = y - 2( Square root the left side ) ±√x = y( Add 2 to both side to isolate y )

Example Graph of Quadratics~ y = x²( Original )~~~> x = y²( Inverse ) Cool Huh? :P

Example Problems~ The Cubic Equation y = x³ + 4 ♠ a cube function x = y³ + 4 ♠ x and Y rotate x - 4 = y³ ♠ add 1 both side ³√(x-4) = y ♠ and square root

Table using the equation ~ y = x³ + 4 Table equation 1 Table equation

Practice problems!~ 1) y = 2x - 52) y = x + 1 3) y = x² - 4x + 5 4) y = 2x³ - 3

ANSWERS! 1) y = (x + 5) / 2 2) y = x - 1 3) y = ±√x ) y = ±√(x+3) / 2

Finish ~