Unit 7 – Rational FunctionsTopic: Transformations of the Rational Parent

Function

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.

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Transforming the Rational Parent FunctionGeneral 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}

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Identify the asymptotes, domain & range for the given function, then sketch the graph of the function.

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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

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.

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Transforming the Rational Parent Function

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.

HomeworkTextbook Section 8-4 (pg. 597): 2-7, 17-22

Due 2/24