312 CHAPTER 2 Graphs and Functions Chapter 2Test Prep New Symbols 1a, b2 ordered pair ƒ1x2 function ƒ evaluated at x (read “ƒ of x” or “ƒ at x”) x change in x y change in y m slope Œ x œ greatest integer less than or equal to x ƒ° g composite function Key Terms 2.1 ordered pair origin x-axis y-axis rectangular (Cartesian) coordinate system coordinate plane (xy-plane) quadrants coordinates conditional statement converse collinear graph (of an equation) x-intercept y-intercept 2.2 circle radius center (of a circle) 2.3 dependent variable independent variable relation function input output input-output (function) machine domain range increasing function decreasing function constant function relative minimum absolute minimum 2.4 linear function constant function standard form relatively prime slope rise run average rate of change secant line mathematical modeling linear cost function revenue function profit function 2.5 point-slope form slope-intercept form negative reciprocals scatter diagram linear regression zero (of a function) 2.6 continuous function parabola vertex inflection point piecewise-defined function step function 2.7 symmetry even function odd function vertical translation horizontal translation 2.8 difference quotient composite function (composition) Quick Review Concepts Examples 2.1 Rectangular Coordinates and Graphs Distance Formula Suppose that P1x1, y12 and R1x2, y22 are two points in a coordinate plane. The distance between P and R, written d1P, R2, is given by the following formula. d1P, R2 =!1x2 −x12 2 + 1 y 2 −y12 2 Find the distance between the points P1-1, 42 and R16, -32. d1P, R2 = 236 - 1-1242 + 1-3 - 422 = 249 + 49 = 298 = 722 298 = 249 # 2 = 722 Find the coordinates of the midpoint M of the line segment with endpoints 1-1, 42 and 16, -32. M= a -1 + 6 2 , 4 + 1-32 2 b = a 5 2 , 1 2b Midpoint Formula The coordinates of the midpoint M of the line segment with endpoints P1x1, y12 and Q1x2, y22 are given by the following. M= a x1 +x2 2 , y1 +y2 2 b
RkJQdWJsaXNoZXIy NjM5ODQ=