Name: Date assigned: Band:______ Precalculus | Packer Collegiate
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Name:_______________________ Date assigned:______________ Band:________ Precalculus | Packer Collegiate Institute Rational Functions #4 Warm Up 1: SKETCHES A sign analysis tells you where a function is positive or negative. The only ways a function can switch from being positive to being negative (or being negative to being positive) are at x-intercepts, vertical asymptotes, and holes. However, we have seen that just because a function might switch signs at x-intercepts, they don’t have to switch signs. Below you are going to draw quick sketches of examples of functions with the following properties… x-intercept at x=2 VA at x=2 Switches from – to + at x=2 Switches from + to – at x=2 Stays – at x=2 Stays + at x=2 Warm Up 2: I have the function p( x) (2 x 5)( x 1) . ( x 1) (a) What would this function look like when graphed? (b) There is a hole on this graph. What is the height of the hole? 1 Hole at x=2 Section 1: From a graph to a sign analysis, and vice versa… 1. Draw a sign analysis for the following graph… y x 2. A function has the sign analysis below and a horizontal asymptote at y 1 . Come up with a potential sketch! (Hint: Draw the VA and HA dashed lines first! That helps!) y 2 x 3. A function has the sign analysis below and a horizontal asymptote at y 3 . Come up with a potential sketch! (Hint: Draw the VA and HA dashed lines first!) y x 4. A function has the sign analysis below and no horizontal asymptote. (a) What is the end behavior? (b) Come up with a potential sketch! y x 3 Section 2: Graphing Rational Functions from Scratch x 2 ( x 2)( x 3) 1. Analyze f ( x) ( x 1)2 ( x 3) (a) Find the holes, VAs, and x-intercepts. Also, answer what the domain of the rational function is. (b) Determine the end behavior (Is there a HA? If not, what’s the graph going to be doing for large positive and negative values?) (c) Do a sign analysis of the function! (d) Do a quick sketch! y 4 x Section 3: Problems Come up with a decent sketch of the rational functions below. Check your graphs on Geogebra or your graphing calculator. Both won’t show you holes, however. Ah, computers. Inferior to the human mind. (1) f ( x) x2 1 x2 2 x 3 y x (2) g ( x ) x2 x 1 y 5 x (3) R ( x ) 3x 3 2x 4 y x (4) y x 1 x2 9 y 6 x (5) y x 2 x 12 x2 4 y x (6) k ( x) 5 4x x2 x5 y 7 x (7) f ( x) x 2 4 x 12 x4 y x (8) y x x 9x 3 y 8 x g ( x) (9) x 1 x2 1 y x (10) y x2 1 x y 9 x (11) y x 1 [hint: rewrite] x y x (12) f ( x) x4 1 x2 4 y 10 x
