Unit 7 – Rational Functions

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. Transforming the Rational Parent Function • 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.

5. Transforming the Rational Parent Function • 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.

6. Journal EntryTITLE: 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