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MCR3U1 EXPLORING PROPERTIES OF PARENT FUNCTIONS U2L3 PART A ~ INTRODUCTION Every function can be classified as a member of a family – a collection of functions sharing common characteristics. LINEAR QUADRATIC y=x y = 5x y = 3x – 4 y = ¼x + 5 y = x2 y = 3(x – 2)2 + 4 y = x2 + 5x + 6 y = (x – 3)(x + 4) Different functions, but same family! PART B ~ DEFINITIONS parent function: the simplest, or base, function in a family ex. f(x) = x, g(x) = x2, etc. asymptote: a line that the graph of a relation or function approaches but never touches; it can be a vertical, horizontal, or oblique axis of symmetry: a line that divides a figure into 2 congruent parts PART C ~ GRAPHING THE PARENT FUNCTIONS BY TABLE OF VALUES Equation of Function f(x) = x f(x) = x2 Table of Values x y 2 1 0 –1 –2 x 2 1 0 –1 –2 y Sketch of Graph y x y x MCR3U1 U2L3 f (x) x 1 f (x) x x 0 1 4 9 16 y x 3 y y x y 2 1 x 1 2 1 3 0 1 3 1 2 –1 –2 –3 f (x) x x 2 1 0 –1 –2 Y y x MCR3U1 U2L3 PART D ~ SUMMARY Equation of Function Name of Function Sketch of Graph Special Features/ Symmetry y f(x) = x x y f(x) = x2 x y f (x) x x y f (x) 1 x x y f (x) x x Domain {…} Range {…} passes through the origin (0,0) slope is equal to 1 divides the plane in half diagonally graph lies in Q1 & Q3 parabola opens up vertex at the origin y has a minimum value y–axis is axis of symmetry graph lies in Q1 & Q2 half parabola opens to the right starts at the origin x and y have minimum values graph lies in Q1 hyperbolic in shape x– and y–axes are asymptotes lines y = x and y = –x are axes of symmetry graph lies in Q1 & Q3 graph opens up vertex at the origin y has a minimum value y–axis is axis of symmetry graph lies in Q1 & Q2 HOMEWORK: p.28 #1, 2, 3