1 / 8

Transformations of graphs

Transformations of graphs. Trig Functions. Features of trig parent graphs. Amplitude. y = a trig x Equation:| a | = amplitude Amplitude is defined for sin and cos only Graph: amplitude = (peak – trough)/2 Transformation: vertical stretch/shrink/reflection

caden
Download Presentation

Transformations of graphs

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. Transformationsof graphs Trig Functions

  2. Features of trig parent graphs

  3. Amplitude • y = a trig x • Equation:| a | = amplitude • Amplitude is defined for sin and cos only • Graph: amplitude = (peak – trough)/2 • Transformation: vertical stretch/shrink/reflection • Circle: amplitude equals radius

  4. Period • y = trig (bx) • Normal period for sin, cos, csc and sec is 360˚ or 2π • Normal period for tan and cot is 180˚ or π • Equation: Actual period = Normal period/b Graph: period equals distance between cycles; b = number of cycles between 0˚ and 360˚ for sin,cos,csc or sec; between 0˚ and 180˚ for tan and cot • Transformation: horizontal stretch/shrink/reflection • Circle: b changes rate of rotation (think of gears or pulleys)

  5. Phase shift • y = trig(bx + c) • Equation: Phase shift = -c/b • Graph: horizontal shift (left if c is pos; right if neg) • Circle: Starting at a different point on the circle

  6. Vertical Displacement • y = trig x + d • Equation: Vertical displacement = d • Graph: vertical shift (up if d is pos; down if neg) d = distance that the x-intercepts of the parent graph moved up or down • Circle: The entire circle is moved up or down

  7. Summary of transformations on a rectangular graphy = a trig (bx + c) + d • a • Vertical stretch if |a| > 1 • Vertical shrink if |a| < 1 • Vertical reflection if a < 0 • b • Horizontal shrink if |b| > 1 • Horizontal stretch if |b| < 1 • Horizontal reflection if b < 0 • c • Horizontal shift: left if c > 0, right if c < 0 • d • Vertical shift: up if d > 0, down if d < 0

  8. Summary of trig calculationsy = a trig (bx + c) + d • Amplitude = |a| • Actual period = normal period / |b| • normal period for sin, cos, csc and sec is 360˚ or 2π • normal period for tan and cot is 180˚ or π • Phase shift = -c / b • Vertical displacement = d Finding values from a graph • | a | = amplitude = (peak – trough) / 2 • b = number of cycles between 0 ˚ and 360˚ for sin,cos,csc and sec; between 0 ˚ and 180˚ for tan and cot • c = k * -b where k is the x-value of the point where the y-intercept has moved to • d = distance that the x-intercepts of the parent graph moved up or down

More Related