Chapter 1

1. Chapter 1 1-3 Transforming Linear functions

2. Warm up Instructions: Name the parent function of the following problems: 1. 2. 3. 4.

3. Warm up answer Instructions: Name the parent function of the following problems: 1. Answer: Quadratic Function 2. Answer: Rational Function 3. Answer: Linear function 4. Answer; Square root function

4. Objectives • The student will be able to: • Transform linear functions • Solve problems involving linear transformations

5. Transforming linear Functions • What is a transformation? • Answer: A transformation is a change in the position, size, or shape of a figure or graph. • What is a Linear function? • Answer: is a function, meaning we have an input and an output, that can be written in the form . Its graph is a line. • If we transforming linear functions , we can say we are changing the linear function either the way it looks in the graph or the equation.

6. Transforming Linear Functions • There are four ways we can transform the linear function by : • Just remember the x changes

7. Transforming Linear functions Just remember y changes

8. Transforming linear functions Just remember y is the mirror so the one that changes is the x

9. Transforming Linear functions Just remember x is the mirror so the one that changes is the y

10. Example 1 • Let g(x) be the indicated transformation of f(x).Write the rule for g(x). • ; g(x) is a horizontal shift 3 units to the right. • Solution: • subtract 3 from the input • evaluate f at x-3

11. Example 2 • Let g(x) be the indicated transformation of f(x).Write the rule for g(x). • ; g(x) is reflected about the y-axis. • Solution: • change the input of f • simplify

12. Student practiceExample 3 • Let g(x) be the indicated transformation of f(x).Write the rule for g(x). • ; g(x) is a vertical shift (vertical translation) 3 units down.

13. Student PracticeExample 4 • Let g(x) be the indicated transformation of f(x).Write the rule for g(x). • ; g(x) is a reflection across the x-axis.

14. Lets combine transformationsExample 5 • Let g(x) be the indicated transformation of f(x).Write the rule for g(x). • ; g(x) is a vertical shift (vertical translation) 3 units down followed by a reflection across the x-axis • .Solution: • First lets take care of the vertical translation • substitute • simplify

15. Example 5 continue • Then we continue with the reflection across the x-axis

16. Stretches and compression • Stretches and compressions change the slope of a linear function. If the line becomes steeper, the function has been stretched vertically or compressed • horizontally. If the line becomes flatter, the function has been compressed vertically or stretched horizontally.

17. Stretches and compressions

18. Example 6 • Let g(x) be a vertical compression of f(x) = 3x + 2 by a factor of 4 . Write the rule for g(x) and graph the function. • Solution: • Vertically compressing f(x) by a factor of replaces each f(x) with a · f(x) where a = 4. • substitute • simplify

19. Student PracticeExample 7 • Let g(x) be a horizontal compression of f(x) = 5x - 2 by a factor of 1/3 . Write the rule for g(x) and graph the function.

20. Now lets put everything together Example 8: Let g(x) be a horizontal compression of f(x) = 6x- 5by a factor of 1/3 followed by a vertical translation 4 units up . Lets h(x) be the horizontal compression and g(x) the vertical translation. Write the rule for g(x) and graph the function.

21. Example 8 continue • Now lets take care of the translation • substitute • simplify

22. Student practice • Do all worksheet

23. Homework • Page 28 from book • problems 2 to 6 and 12 to14.

24. Closure • Today we talked about transforming linear functions through translating and reflecting . • Tomorrow we are going to see scatter plots and the best fit line.

25. Have a great day!!!