aeldainur - TT -1t FIGURE 2.2.27 Graph for Problem 37 bus A oodw Shiud 011alai 6 FIGURE 2.2.28 Graph for Ew radw (1 Problem 38 Des1010i In Problems 39-42, find an equation of the final graph after the given transforma- tions are applied to the graph of y = f(x). te 2 39. the graph of f(x) 40. the graph of f(x) = x/3. right 2 units 41. the graph of f(x) = x* reflected in the x-axis, then shifted left 7 units 42. the graph of f(x) = 1/x reflected in the y-axis, then shifted left 5 units and ПЕСТ .3 x' shifted up 5 units and right 1 unit stretched vertically by a factor of 3 units, then shifted %3D down 10 units In Problems 43-46, describe in words how the graph of the first function is obtained from the graph of the second function using rigid and nonrigid transformations. Carefully graph the first function. FErrot 43. y = -1 + 2V-x + 2; y = Vx 44. y = 2 + ¿(-x)³; y = x', %3D %3D 1 1 45. y = 2 46. y = -1 - x - j' Y = (x - 2)2i y = ! MUR 1AN 69 2.2 Symmetry and Transformations

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.