1/100 Range: 1/10 1/ 2. 1) Constant: choose a value for the constant that can be graphed on the coordinate grid below.

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1 Name 1) Constant: choose a value or the constant that can be graphed on the coordinate grid below a y Toolkit Functions Lab Worksheet thru inverse trig ) Identity: y ) Reciprocal: 1 ( ) y / 1/ 1/1 1/ 1 Vertical Asymptote: 1 Horizontal Asymptote: 1 4) Absolute Value:,, y

2 5) Quadratic: (even power) 6) Square Root: y y Range: 5 6 7) Cubic: (odd power) 8) Cube Root: y y

3 9) Eponential: (use base, let b=) b y 4 Asymptote: 5 1) Logarithmic: (use base, let b=) log b y 1/8 1/ 4 1/ 4 8 Asymptote: 16 11) Greatest Integer: int( ) y Range: ) Signum Function: ( ) y 4 Range: 1 4

4 1) Trigonometric: ( ) sin y / / Range: / / 14) Reciprocal Trigonometric: csc y / / Range: / / Asymptotes: scale : / y scale :1 scale : / y scale :1 15) Trigonometric: cos y / / Range: / / 16) Reciprocal Trigonometric: sec y / / Range: / / Asymptotes: scale : / y scale :1 scale : / y scale :1

5 17) Trigonometric: tan y / 4 / /4 Range: /4 / / 4 Asymptotes: 18) Reciprocal Trigonometric: ( ) cot y / 4 / /4 Range: /4 / / 4 Asymptotes: scale : / y scale :1 scale : / y scale :1 Inverse Trigonometric Functions: Sketch the inverse trig unctions, labeling clearly the aes, endpoints & asymptotes ) y sin ) y cos 1) y tan Range: Range: Range: Highlight the portion o the unit circle which identiies the range o each inverse trig unction. Include open or closed circles identiying inclusive or eclusive angles.

6 AB Calculus: Polynomial Functions and Inequality Solutions Rational Function Inequalities Learning Target: I can graph polynomials with roots o multiplicity, recognize local & global behavior, and solve inequalities. I can solve rational inequalities by using the graph o the related polynomial. A) Graph the polynomial unction on the aes provided where A. B) State the end-behavior by completing the limit statements. C) Use the graph to state the intervals or on which the polynomial is greater than or equal to zero using correct mathematical notation. D) Solve the rational inequality where A & B. Polynomial Inequality Graph o Polynomial Function Rational Inequality 1) A 4 A 4 lim lim B Solve ) A 4 1 Solve ) 4 1 Solve 4) 4 1 Solve 5) 4 1 Solve 6) 4 1 Solve 7) 4 1 Solve lim ( ) A 4 1 lim ( ) B A 4 1 lim ( ) B 4 1 B lim ( ) A A 1 4 lim ( ) B 1 B 4 lim ( ) A A 4 1 lim ( ) B

7 AB Calculus: Rational Functions and Basic Transormations Learning Target: I know how to 1) Identiy characteristics o a rational unction rom graph and equation. Characteristics include: vertical asymptotes, horizontal or oblique asymptotes, holes, -intercept(s) and y-intercept. ) Write an equation or a rational unction by identiying the horizontal asymptote, vertical asymptotes and the behavior o the graph near each VA. 1 Here is the toolkit unction or the rational unction ( ). Transormations o this unction in terms o the equation g( ) A B C D are eactly the same as transormations you have done or all toolkit unctions like,, concerned that you know ( ) and. Generally speaking, Mrs. Eagen will only be g A C D or the rational unction transormations. When you draw your graphs you will include the vertical and horizontal asymptotes as dashed lines, oblique or slant asymptotes as dashed lines, and holes as open circles. 1 Basic Transormations o the Rational Function: Given the graph o the rational unction: ( ), sketch on the same grid the basic transormation given by the equation. 1 1) g( ) ) 1 g( ) ) 1 g( ) Sketch in the vertical and horizontal asymptotes then write these equations or the rational unctions. Let A=1. 4) 5) 6) 7) 8) 9) AB Calculus: Rational Functions and Equivalent Forms

8 Learning Target: I can 1) Re-epress a rational unction using algebraic techniques: actoring & division. numerator product o actors remainder y y y quotient denominator product o actors divisor ) Identiy when a hole occurs and the (, y) coordinate o hole rom actored orm. ) Recognize the Quotient as the end behavior asymptote, either the horizontal or oblique asymptote. 5 (5)( 1) 1) ( ) 11) ( ) 1) 1) ( ) ( )( 1) ( ) Rewrite: Factor: Rewrite: VA: HA/OA: Range: Evaluate: 1 Hole: Hole: Hole: Y-intercept: X-intercepts: Sketch: AB Calculus: Rational Functions and End Behavior

9 m m1 a a1... am 1 am Learning Target: Given a rational unction, y I can use the end-behaviormodel to determine the long-run end-behavior o the graph and decide i the rational unction has: n n1 b b1... bn 1 bn o a horizontal asymptote at y o a horizontal asymptote at y c where c is a constant. o an oblique asymptote modeled by the end-behavior model given by: y a m. n b Eamine the ollowing rational unctions and complete part a, b, c & d or each. a) Write an end-behavior model or each rational unction. Simpliy by reducing common actors when possible. b) Complete the behavior phrases: " as, y " or " as, y " or each EBM. c) Complete long division, and re-epress the rational unction as: remainder y quotient. divisor d) Compare the end behavior model rom part (a) and the quotient rom part (b). 14) ) ) Summarize your conclusions rom the eamples above. m m1 a a1... am 1 am Given a rational unction y n n1 b b1... bn 1 bn the end-behavior model is. o The graph will have a horizontal asymptote at y when. o The graph will have a horizontal asymptote at when. o The graph will have an oblique asymptote o when. An oblique asymptote is also called a slant asymptote. Use your short-cuts rom the summary to state the ollowing or each rational unction. o end-behavior model o complete the behavior phrases: " as, y " or " as, y " o 17) horizontal asymptote, i applicable ) )

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