Download presentation

Presentation is loading. Please wait.

Published byJamil Power Modified over 4 years ago

1
Unit 7 – Rational Functions Topic: Transformations of the Rational Parent Function

2
Rational Parent Function Graph of the rational parent function is a hyperbola. Vertical asymptote at x = 0; D: {x | x ≠ 0} Horizontal asymptote at y = 0; R: {y | y ≠ 0} Asymptote: boundary line for the graph of the function.

3
Transforming the Rational Parent Function General format of a rational function: Possible transformations (we’ve done this before): ◦ |a| > 1: stretches hyperbola away from origin. ◦ |a| < 1: compresses hyperbola towards origin. ◦ a < 1: reflects graph across x-axis. ◦ h (“bad child”): translates function left or right. Moves the vertical asymptote. Vertical asymptote is the line x = h; D: {x | x ≠ h} ◦ k (“good child”): translates function up or down. Moves the horizontal asymptote. Horizontal asymptote is the line y = k: R: {y |y ≠ k}

4
Identify the asymptotes, domain & range for the given function, then sketch the graph of the function. V. asymptote: x = –2 (remember to change the sign for h) H. asymptote: y = 4 D: {x | x ≠ –2}; R: {y | y ≠ 4} Plot asymptotes Since everything shifted left 2 & up 4, the points (1, 1) & (– 1, –1) from the parent function are now (–1, 5) & (– 3, 3). Plot these points. Sketch the resulting hyperbola through those points. Transforming the Rational Parent Function

5
Using the rational parent function as a guide, describe the transformations and graph the function. The function will translate 3 units right (“bad child”) and 6 units down (“good child”) from the parent function. V. asymptote: x = 3 H. asymptote: y = -6 Plot anchor points and sketch the function. Transforming the Rational Parent Function

6
Journal Entry TITLE: Rational Functions 3-2-1 Identify 3 things you already knew from the Powerpoint, 2 new things you learned, and one question you still have.

7
Homework Textbook Section 8-4 (pg. 597): 2-7, 17-22 Due 2/24

Similar presentations

OK

Functions: Transformations of Graphs Vertical Translation: The graph of f(x) + k appears as the graph of f(x) shifted up k units (k > 0) or down k units.

Functions: Transformations of Graphs Vertical Translation: The graph of f(x) + k appears as the graph of f(x) shifted up k units (k > 0) or down k units.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google