Fichas
Func n R: How to draw fancy equations.
Fichas del conjunto (7)
- 1Func n' R: How to graph fancy functions!
- 2What 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.
- 3How 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
- 4How 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
- 5Trick! 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).
- 6How 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.
- 7How 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.
Información
- Descripción
- How to draw fancy equations using the knowledge of multiplicities and roots.
- Creado por
- Lauren Jatana
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- 63
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