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Description
| Question | Answer |
| Func n' R: How to graph fancy functions! | |
| What is a multiplicity? And how can it help? | A multiplicity is the NUMBER of times a ROOT/X-INTERCEPT/FACTOR appears in a function. I.e. Does it have each root once or twice or three times? etc. |
| How does a fancy function behave when it has an even # of roots? | If it has even: it changes direction, if was going down, 'bounces' off x and goes up now. Think x^2 |
| How does a fancy function behave when it has an odd # of roots? | If it is odd: It "enters" to the other realm past the the x-axis and keeps the same direction. If it was going down, it keep going down. Think x^5 |
| Trick! When I am given a graph, and need to find the function... what do I need to remember? | I can see two roots at 2, and one at -1 so my equation is (x-2)^2*(x+1) right? Wrong. You are forgetting to check for a vertical stretch factor (that would still give the same roots! as that. This one has a VSF of 3) So it would be 3*(x-2)^2*(x+1). |
| How many roots does f(x)=x^3-2x+1 have? | The "term" with the biggest exponent is x^3, therefore it should have 3 roots. |
| How many roots does f(x)=(x+2)^3(x-2) have? What is the multiplicity of each root? | It has four roots, because it boils down to (x^3) * (x) = x^4 total. (x+2) root has a multiplicity of 3, and (x-2) root has a multiplicity of 1. |
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