314 CHAPTER 2 Graphs and Functions Concepts Examples 2.5 Equations of Lines and Linear Models Summary of Forms of Linear Equations Equation Description y =mx +b Slope-Intercept Form Slope is m. y-intercept is 10, b2. y −y1 =m1x −x12 Point-Slope Form Slope is m. Line passes through 1x1, y12. Ax +By =C Standard Form 1A, B, and C integers, A Ú 0.2 Slope is - A B 1B≠02. x-intercept is AC A , 0B 1A≠02. y-intercept is A0, C BB 1B≠02. y =b Horizontal Line Slope is 0. y-intercept is 10, b2. x =a Vertical Line Slope is undefined. x-intercept is 1a, 02. Consider the following equations. y = 3x + 2 3 Slope-intercept form The slope m is 3, and the y-intercept is A0, 2 3B. y - 3 = -21x - 42 Point-slope form The slope m is -2. The line passes through the point 14, 32. 4x + 5y = 7 Standard form with A = 4, B = 5, C = 7 The slope is m= - A B = - 4 5 . The x-intercept has C A = 7 4 and is A 7 4 , 0B. The y-intercept has C B = 7 5 and is A0, 7 5B. y = -6 Horizontal line The slope is 0. The y-intercept is 10, -62. x = 3 Vertical line The slope is undefined. The x-intercept is 13, 02. 2.6 Graphs of Basic Functions Basic Functions ƒ1x2 =x Identity Function ƒ1x2 =x2 Squaring Function ƒ1x2 =x3 Cubing Function ƒ1x2 =!x Square Root Function ƒ1x2 =!3 x Cube Root Function ƒ1x2 = ∣ x ∣ Absolute Value Function ƒ1x2 = Œ x œ Greatest Integer Function Refer to the function boxes in Section 2.6. Graphs of the basic functions are also shown on the back inside cover of the print text. Consider the following graphs. 2.7 Graphing Techniques Stretching and Shrinking If a 71, then the graph of y =aƒ1x2 is a vertical stretching of the graph of y = ƒ1x2. If 0 6a 61, then the graph of y =aƒ1x2 is a vertical shrinking of the graph of y = ƒ1x2. If 0 6a 61, then the graph of y =ƒ1ax2 is a horizontal stretching of the graph of y = ƒ1x2. If a 71, then the graph of y =ƒ1ax2 is a horizontal shrinking of the graph of y = ƒ1x2. 4 –4 x y 0 y = √x y = –2√x The graph of y = -22x is the graph of y = 2x stretched vertically by a factor of 2 and reflected across the x-axis.
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