1. Warm Up 1. State whether the following functions are even, odd, or neither: a. f(x) = –3x 2 + 4 b. f(x) = 2x 3 – 4x 1. State the intervals in which the function is increasing, decreasing, and constant.

8. Math IV Lesson 4 Essential Question: How do you write equations and draw graphs for the simple transformations of functions? Section objectives: Students will study the effects of translations, reflections, stretches and shrinks on the equations and graphs of functions. Standards : MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. b. Investigate transformations of functions. c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition. Math IV Lesson 4 Essential Question: How do you write equations and draw graphs for the simple transformations of functions? Section objectives: Students will study the effects of translations, reflections, stretches and shrinks on the equations and graphs of functions. Standards : MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. b. Investigate transformations of functions. c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

9. New Vocabulary 1. Vertical shift c units up h(x) = f(x) + c 2. Vertical shift c units down h(x) = f(x) – c 3. Horizontal shift c units right h(x) = f(x-c) 4. Horizontal shift c units left h(x) = f(x+c) 5. Reflection in the x-axis h(x) = -f(x) 6. Reflection in the y-axis h(x) = f(-x) 7. Horizontal shifts, vertical shifts, and reflections are called rigid transformations because the shape of the graph is unchanged.

10. New Vocabulary Continued 8. Nonrigid transformations change the shape of the graph. 9. A nonrigid transformation of the graph y = f(x) is represented by y=cf(x), where the transformation is a vertical stretch if c > 1 10. A nonrigid transformation of the graph y = f(x) is represented by y=cf(x), where the transformation is a vertical shrink if 0 < c < 1 11. A nonrigid transformation of the graph y = f(x) is represented by h(x) = f(cx). If c > 0 it is a horizontal shrink. 12. A nonrigid transformation of the graph y = f(x) is represented by h(x) = f(cx). If 0 < c < 1 then it is a horizontal stretch

11. 1.4 Shifting, Reflecting, and Stretching Graphs  In order to graph you need to be familiar with the six most commonly used functions in algebra

12. F(x) = x

14. Graph number 3

18. Vertical and Horizontal shifts Outside of parentheses moves up or down. Inside of parentheses moves opposite and left or right. Lets use standard parabola guy and move him around. If we want to move him up 2 units we do this: f(x) = x 2 + 2

19. Or we can move him down 2 units f(x) = x 2 -2

20. Or we can move him left 2 units Remember left and right movements are inside the parentheses and do the opposite. f(x) = (x+2) 2

21. Or we can move him right 3 units Remember left and right movements are inside the parentheses and do the opposite. f(x) = (x -3) 2

22. F(x) = (x - 2) 2 + 1

23.  You can either reflect across the x axis Or the y axis 1. Reflection in the x –axis: h(x) = -f(x) 2. Reflection in the y-axis: h(x) = f(-x)

25. This is a vertical stretch

26. F(x) = 1/3 (x) 2

27. F(x) = (2 x) 2

28. F(x) = (1/2 x) 2