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precalc unit 2 test
| Question | Answer |
|---|---|
| point of inflection: | any time when a function changes from concave up to concave down (or vice versa)/the rate of change changes from increasing to decreasing (or vice versa) |
| rate of change increases = | concave up |
| rate of change decreases = | concave down |
| when a function has a global/absolute minimum: | even degree, positive coefficient |
| when a function has a global/absolute maximum: | even degree, negative coefficient |
| when a function does not have a global maximum or global minimum: | odd degree |
| when it asks for open intervals/anything with concavity: | ( ) |
| be careful if the question asks to find: -all zeros -imaginary zeros -real zeros | ok!! |
| what to say w/ a table question that asks for the degree: | f(x) has a degree of # because the 1st/2nd/3rd/etc difference is a constant of # over consecutive equal length input value intervals |
| remember: | you can only say "consecutive equal length input value intervals" when the y-value is actually consecutive!!! |
| what to say w/ a table question when you cannot determine the degree: | f(x) cannot be determined. We do not have any constant differences |
| rule with an additional negative sign in a sign chart or a ^2,3,etc | extra negative in the front: add a negative answer to all of the parts of the sign chart ^2,3,etc: write down the factor that many times to be included more than once of the sign chart |
| mrs. alwood's rule: | when YOU draw a square root, YOU draw a ± !!! |
| end behaviors when it is odd and + | left: -∞ right: ∞ |
| end behaviors when it is odd and - | left: ∞ right: -∞ |
| end behaviors when it is even and + | left: ∞ right: ∞ |
| end behaviors when it is even and - | left: -∞ right: -∞ |
| even function: | -symmetrical over the y-axis f(-x) = f(x) -if you were to fold your paper in half, it would be equal ex: (-2,-3) and (2,-3) -only the x-value switches sign |
| odd function: | -symmetrical over the origin (0,0) g(-x) = -g(x) -if you were to fold the paper in half both ways, it would be equal ex: (-2,2) and (2,-2) -both values switch signs |
| what to say when a function has even/odd/neither symmetry: | therefore, f(x) has even/odd/neither symmetry |
| if ≥ or ≤ is in your problem, than ________ must be in your answer!!! | ALL the zeros |
| degree = | how many zeros/x-intercepts there are |
| average rate of change formula: | f(b) - f(a) / b-a |
| horizontal/slant asymptote for equal heavy: | horizontal asymptote w/ coefficients divided |
| horizontal/slant asymptote for bottom heavy: | horizontal asymptote at y = 0 |
| horizontal/slant asymptote for top heavy: | slant asymptote using long division (if the degree on the numerator is exactly 1 more than the degree of the denominator but it will ask you to find the slant asymptote so dont worry about that) |
| remember when solving rational equations: | before you solve, (cross-multiply or making it into one fraction) check for extraneous solutions!!! |
| rational function = | has vertical AND horizontal asymptote |
| anything to the zero power is... | 1!!! |
Created by:
acuda25