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AP-pre cal
| Question | Answer |
|---|---|
| Sequence | is a function from the whole numbers to the real numbers. |
| Discontinosus/ discrete graphs | When a sequence is graphed and the points on the graph cannot be connected to form a line or a curve. |
| arithmetic sequence formula | an = ak +d (n - k) |
| arithmetic sequence | behave like linear functions,execpt they are not continuous and slope is always the same |
| Successive terms | have a common difference |
| Geometirc sequence | has successive terms that have a common ratio( term is multiplied by the same number to get the second term. |
| Geometirc sequence formula | gn=gk(r)^(n-k) |
| where d= ak= | common difference kth term |
| rational function | quotient of two polynomials |
| hole | when the same factor appears in both the top (numerator) and bottom (denominator) of the equation. |
| vertical asymptope | occurs when a factor in the denominator cannot cancel out with factors in the numerator |
| end behavior for rational functions | The end behavior of a rational function is determined by the leading terms of the numerator and denominator:f(x)=ax^n/bx^d |
| end behavior 1: the leading terms have the same degree(n=d) | f(x) has a horizontal asymptope :y=a/b |
| end behavior 2: The denominator dominates the numerator(n<d) | f(x) has a horizontal asymptope: y=0 |
| end behavior 3the numerator dominates the denominator(n>d) | f(x) has the end behavior of the polynomial y=(a/b)x^n-d |
| End behavior note:if the degree of the numerator is exactly 1 more than the degree of the denominator | f(x) has a slant asymptote |
| Let f(x)= g(x)/h(x) be a rational function where g(x)&h(x) have no factors in common | 1.f(x) has zeros when g(x)=0 2.f(x) is undefined h(x)=0 |
| transformations:g(x)=f(x)+k | y moves up /down(vertical translation) |
| transformations:g(x)=f(x+h) | x moves left/right(horizontal translation) |
| transformations: g(x)= af(x) | y moves multipled by a number up/down(vertical dialation) Note:if a<0, f is reflected over x-axis |
| transformations:g(x)=f(bx) | x mutliplied by 1/b left/right Note:if b<0, f is reflected over y-axis |
| End behavior | What happens to f(x)(hight) as x increases/decreases without bound |
| left end behavior: lim f(x) x→-∞ | As x decreases without bound, the y values of f(x).... |
| right end behavior: lim f(x) x→∞ | As x increases without boun, the y values of f(x)..... |
| Polynomial end behavior: Right side | 1. goes to positive infinity if leading coefficient is positive 2.goes to negative infinity if leading coefficient is negative |
| Polynomial end behavior: Left side | 1.goes in the same direction as the right if the degree is even 2. goes in the opposite direction as the right if the degree is odd |
| exponential Growth | F(x)=a(b)^x, a is more than 0 &b is more than 0.a cannot = 0 and b cannot = 1 |
| Increasing Vs. Deceasing | Exponential is always increasing/decreasing.They'll never switch, so have no relative extrema |
| Concave up Vs. Down | Exponential |
| a b | represents the initial amount. represents the common ratio (a is less than zero than it's below the x-axis) |
| End behavior for exponential functions | for exponential functions in general form, as the input values(x) increase/decrease without bound, the output values(y) will increase/decrease without bound or they will approach zero. |
| product property | b^m(b^n)=b^(m+n) |
| power property | (b^m)^n=b^(m*n) |
| negative exponent property | b^-n=1/b^n |
| reverse property is | b^(m*n)=(b^m)^n |
| how to get (x)reggression | 1. go to lists&speadsheets 2.type in the numbers 3. Menu,4,1 |
| residual | Actual Output value- Predicted Output value (positive value means undershoot and negative value means overshoot) |
| Linear model | when the graph has a constant rate of change |
| Quadratic model | When the rate of change are increasing/decresing at a constant rate |
| Exponential model | When the output values are roughly proportianal (Each succesive output is the result of repeated multiplication) |
| point-Intercept Form | f(x)=yi+m(x-xi) |
| Slope-intercept Form (linear Functions) | f(x)=b+mx |
| exponential functions | f(x)=ab^x |
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