Transformations of Graphs and Inverses Unit 3 Day 11 Transformations of Graphs and Inverses

Warm Up continued -> Day 11 Warm Up How are the following graphs changed from their parent graph, y = x2? (If you don’t remember some of the transformations, graph the equation and the parent in the calculator  ) 1) y = (x – 4)2 y = x2 – 4 3) y = x2 + 1 y = (x + 3)2 y = 4x2 y = ½ x2 y = 3(x - 4)2 8) y = 1/4 x2 + 3 Warm Up continued ->

Amount of radio-active material Day 11 Warm Up Time Amount of radio-active material ½ 1 2 3 4 8 5 16 9) Use the following data to graph on each of the following coordinate planes. Be sure to pay attention to the labels on each axis. Explain how the graphs are alike. Are different.

Warm Up continued -> Day 11 Warm Up Answers How are the following graphs changed from their parent graph, y = x2? (If you don’t remember some of the transformations, graph the equation and the parent in the calculator  ) 1) y = (x – 4)2 y = x2 – 4 3) y = x2 + 1 y = (x + 3)2 y = 4x2 y = ½ x2 y = 3(x - 4)2 8) y = 1/4 x2 + 3 Right 4 Vertical stretch by factor of 4 Down 4 Vertical compression by factor of 1/2 Up 1 Vertical stretch by factor of 3 and right 4 Vertical compression by factor of ¼ and up 3 Left 3 Warm Up continued ->

Amount of radio-active material Day 11 Warm Up Answers Time Amount of radio-active material ½ 1 2 3 4 8 5 16 9) Use the following data to graph on each of the following coordinate planes. Be sure to pay attention to the labels on each axis. Explain how the graphs are alike.-Both are curved, level off in one place. Are different. -They are reflections over y=x. 1st flattens at y = 0 and 2nd flattens at x = 0.

Homework Answers After ODM Test p. 12-13 1. b = 10 2. x = 8 a = -4 4. x = -4 r = 28 6. m = 8 k = {0, 8} 8. b = -1 9. x = -2 10. k = 4 p. 12 1. x = 15/2 2. x = {-5, 5} x = -6 4. x = 169 x = {-5, 6} 6. x = 9 7. x = 3 8. x = 7/3

Homework Answers After ODM Test p. 14 11. r = 4 12. b = 1 13. r = 7 14. p = {2, 5} 15. n = 16 16. v = 4 17. n = 7 18. x = {-1, -3} 9. x = 9 10. b = 6

Tonight’s Homework: Complete Packet pg. 15 all and Packet pg. 16 odd

Translations of Exponential Graphs We’ll do the first graph y = 3x together!! y = 0 1/3 1 3 9 27 Domain: _______ Range: ______ All real #’s Display Notes on Document Camera. *Asymptote: a line that a curve approaches as it approaches infinity

Translations of Exponential Graphs On the same grid, graph y = (3)x + 1 using a different color or mark. CLEARLY INDICATE the horizontal asymptote. x y -2 -1 1 2 HA: _____ y = 0 1/3 1 3 9 27 Domain: _______ Range: ______ All real #’s Display Notes on Document Camera. Explain how the graph shifted from the parent graph: Left 1

Practice: Translations of Exponential Graphs You try the others! Complete Notes p. 24 – top p. 26 For each section, split the transformed graphs with your partner! For each graph, add in Then share your info to summarize. Domain: _______ Range: ______ Display Notes on Document Camera.

Bottom of p. 24 SUMMARY of Horizontal Translations Adding “c” in the exponent shifts the graph to the _left_ c units. Subtracting “c” in the exponent shifts the graph to the _right_ c units.

Check Chart on p. 25 -3 1/8 8 -1/8 -2 ¼ 4 -¼ -1 ½ 2 -½ 1 -4 3 -8

SUMMARY of Reflections: p. 26 Negative on x causes the graph to reflect in the opposite direction over the _Y_ axis. Negative on the front of the equation causes the graph to reflect in the opposite direction over the _X_ axis.

Investigation: Inverses Complete Notes p. 26 - 28 Display Notes on Document Camera. Students should complete at least through Notes p. 27 before the You Try at the bottom.

To find inverse functions. Switch the x’s and y’s and solve for y. Ex. 1) Find the inverse of y = 3x + 6 Ex. 2) Find the inverse of y = 5x2

Now Try p. 28 Find the inverses of the functions below. Graph the function and its inverse below. 1) f(x) = x3 2) y = -3x + 4 Have students graph on the board or complete as a class, if time allows.

Now Try p. 28 Find the inverses of the functions below. Graph the function and its inverse below. 3) f(x) = 4) y = 2x Have students graph on the board or complete as a class, if time allows.

Tonight’s Homework: Complete Packet pg. 15 all and Packet pg. 16 odd