Unit 2.2 (5.3 and 5.4) Notes w Review 23-24 KEY

Section 5.3- Parent graphs of y = sqrt(x) and y = root(x, 2) Remember that y= sqrt[n] x^ * is equivalent to y=x, That is why y = sqrt(x) and y = x ^ psi_{2} are the same parent graph. Take your graph transformation packet if you refreshing about the process. 1. Parent graph of y = sqrt(x) or y = x ^ (3/2) Inc: (0,00) or [0, ∞) Dec: Never X 0 1 1 Domain: [0, ∞) 4 9 2+ y 0 2 3 2 5 6 Range: [0, ∞) KEY POINTS ARE: (0,0), (1, 1) and (4, 2). These are the points we move. 2. Parent graph of y = root(x, 3) y = x ^ 10 Inc: (00,00) Dec: Never X -8 -1 0 1 8 y -2 -1 0 1 2 -2 -1+ Domain: (-0,00) Range: (-00, co) KEY POINTS ARE: (-1,-1), (0, 0) and (1, 1). These are the points we move. Examples: 1. Graph: y = - sqrt(2x) + 5 (This is written y = - (2x) ^ 12 + 5 in exponential form) List the transformations in the correct order: 1) Horizontal Shrink by a factor of 2) Reflection over the x-axis 3) Translate up 5 units. Parent: (0,0) (1, 1) (4,2) Trans #1: (0,0) (1/2, 1) (2,2) Trans #2: (0,0) (1/2,-1) (2,-2) Trans #3: (0,5) (1/2, 4) (2.3) Graph the FINAL 3 POINTS and draw parent graph. *** Look in your graph transformation packet if you didn't understand the HORIZONTAL SHRINK. Here is a brief summary: int z=1 (x) -> f(ax) 1fs > 1 then we horizontally shrink by a factor sf * 1/a fa < l then we horizontally stretch by a factor 1/a 2. Graph: y = 3 * root(x + 2, 2) - 4 (This is written y = 3 * (x + 2) ^ (1/2) - 4 in exponential form) List the transformations in the correct order: 1) Translate left 2 units. 2) Vertical Stretch by a factor of 3. 3) Translate down 4 units. Parent: (-1,-1) (0,0) (1,1) Trans #1: (-3,-1) (-2,0) (-1, 1) Trans #2: (-3,-3) (-2,0) (-1,3) Trans #3: (-3,-7) (-2,-4) (-1,-1) Graph the FINAL 3 POINTS and draw parent graph. Describe the Transformations in the proper order. Then graph the square root function. 1. y = sqrt(x + 3) - 4 V / (- 3, - 4) H. translation left 3 units. V. translation down 4 units X New y Down 4 0-3-3 O - 4 = - 4 (-3,-4) 1-3-2 1-4-3 (-2,-3) 4-3 1 2-4-2 (1,-2) D: (- 3, ∞) Inc: [- 3, ∞) or (-3,00) Dec: Never R: (- 4, ∞) 2. y=3 (1/2 * x) ^ v2 +4 V / (0, 4) Y = 3sqrt(1/2 * x) +4 (0,0) (1,1) (4,2) 2 #2 H. Stretch by 2 V. Stretch by 3 (0,0) (2,17 (8,2) 3 13 V. translation up 4 (0,0) (2,3) (8,6) +4 +4 (0, 4)(2, 7) langle8,10) D: [ 0, ∞ rangle R1 [ 4, ∞ rangle Inc: [0, ∞) r\\ (0, infty) Dec: 3. y = 2sqrt(- x) - 4 V / (0, - 4) (0,0) (1,1) (1,2) Reflection over y-axis V.Stretch by 2 *2 *2 *2*2\\ (0, 0)(- 1, 2)(- 4, 4) V. translation down 4 unils - 4/((0, - 4)(- y - 2)(- 4, 0)) D: (- ∞, 0] R / [- 4, ∞) Dec: (-00, 0) or (-00,0] Inc: Never