1 / 30

1.7 Even and Odd Functions Mon Sept 30

1.7 Even and Odd Functions Mon Sept 30. Do Now Let , Find f(-x). Quiz Review. Retakes Last day Friday Let me know today 90% of new score. Even Functions. A function is considered even if, for every x in the domain of f, f(x) = f(-x)

shiri
Download Presentation

1.7 Even and Odd Functions Mon Sept 30

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1.7 Even and Odd FunctionsMon Sept 30 Do Now Let , Find f(-x)

  2. Quiz Review • Retakes • Last day Friday • Let me know today • 90% of new score

  3. Even Functions • A function is considered even if, for every x in the domain of f, f(x) = f(-x) • This tells us that if we plug in opposite x values, we should get the same y value • Even functions are symmetric with respect to the y-axis

  4. Ex • Show f(x) = x^2 + 2 is even

  5. Odd Functions • A function is considered odd if, for every x in the domain of f, f(-x) = -f(x) • This tells us if we plug in opposite x values, we should get opposite y values • Odd functions are symmetric with respect to the origin or the line y = x

  6. Ex • Show f(x) = x^3 + x is odd

  7. Even and odd functions • A function with variables cannot be both even and odd • Always evaluate f(x) and f(-x) and compare the two • A function can be neither even nor od

  8. Another way • Given f(x), evaluate f(-x) and SIMPLIFY: • If you get the exact same thing, f(x) is even • If you can factor out a negative sign and get the original inside, f(x) is odd • If you can’t do either, neither

  9. Ex • Determine whether each of the following functions is even, odd, or neither • 1) • 2)

  10. You try • Determine whether each function is even, odd or neither • 1) • 2) • 3)

  11. Closure • How can you determine whether a function is even, odd, or neither? • HW: p.163-164 #33-47

  12. 1.7 TransformationsTues Oct 1 • Do Now • Graph the following • 1) f(x) = x^2 • 2) g(x) = x^2 + 2 • 3) h(x) = (x + 4)^2 + 2

  13. HW Review: p.163 #33-47

  14. Transformations • A transformation is an operation on a basic function (y = x, x^2, 1/x, etc) that changes the function, but keeps the general behavior

  15. Types of Transformations • Translations • Only moves the function • Reflections • Flips the function • Stretch/Shrink • Changes the shape of the function

  16. Translations • Vertical Translation • For b > 0, y = f(x) + b is y = f(x) shifted up b units y = f(x) – b is y = f(x) shifted down b units • Horizontal Translation • For d > 0, y = f(x – d) is y = f(x) shifted right d units y = f(x + d) is y = f(x) shifted left d units

  17. Ex • Graph the original function, then describe and graph the translation. • 1) f(x) = x^2 - 6 • 2) g(x) = |x – 4| • 3) h(x) = sqrt(x + 2) • 4) p(x) = (x + 2)^2 - 3

  18. Reflections • 2 common reflections: • The graph of y = - f(x) is the reflection of y = f(x) across the x-axis • The graph of y = f(-x) is the reflection of y = f(x) across the y-axis

  19. Ex • Let f(x) = x^3 – 4x^2. Describe how each graph can be compared to f(x) • 1) g(x) = (-x)^3 – 4(-x)^2 • 2) h(x) = 4x^2 – x^3

  20. Vertical Stretch/Shrink • The graph of y = a f(x) will vertically affect f(x) by: • Stretching vertically if |a| > 1 • Shrink vertically if 0 < |a| < 1 • These transformations affect the y-value while keeping the x-coordinate the same

  21. Horizontal Stretch/Shrink • The graph of y = f(cx) can be obtained from the graph of y = f(x) by: • Shrinking horizontally if |c| > 1 • Stretching horizontally if 0 < |c| < 1 • These transformations affect the x-coordinate while keeping the y-coordinate the same

  22. Ex • Ex 6 in the book

  23. Closure • How does each type of transformation affect the original function? • HW: p.164 #49-83 every other odd, 97-113 odds, 119-127 odds • Ch 1 Test Fri Oct 4

  24. 1.7 HW ReviewWed Oct 2 • Do Now • 1) Write an equation for a function that has the shape of y = |x|, but stretched horizontally by a factor of 2, and shifted down 5 units • 2) Write an equation for a function that has the shape of x^3, but upside-down and shifted right 5 units

  25. HW Review p.164

  26. Closure • When only given a graph (x,ycoordinates), how do we apply reflections, translations, and stretch/shrinks? • HW: p.169 #25-31 odds, 53 55 69 71 83-95 odds 101

  27. Ch 1 ReviewThurs Oct 3 • Do Now • Find the domain of

  28. Ch 1 HW Review p.164

  29. Ch 1 Review • 1.1 Distance Formula and Circle Equations • 1.2 Domain and Range • 1.5 Increasing/Decreasing and Max/Mins using a calculator • 1.5 Piecewise Functions • 1.6 Compositions and Decomposing • 1.7 Even and Odd Functions • 1.7 Transformations

  30. Closure • Which of the Ch 1 topics is most difficult for you? Why? • Ch 1 Test tomorrow!

More Related