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

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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 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}

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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

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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

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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.

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

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