Term
|
Definition
If a polynomial f(x) is divided by x - k,
the remainder is r = f(k). |
|
|
Term
|
Definition
| A polynomial f(x) has a factor (x - k) if and only if f(k) = 0. |
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
| The number of positive real zeros of f is |
|
Definition
| either equal to the number of variations in sign of f(x) or less than that number by an even integer. |
|
|
Term
| The number of negative real zeros of f is |
|
Definition
| either equal to the number of variations in sign of f(-x) or less than that number by an even integer. |
|
|
Term
| The line x = a is a vertical asymptote of the graph of f if |
|
Definition
| f(x) approaches infinity or negative infinity as x approaches a, either from the left or the right. |
|
|
Term
| The line y = b is a horizontal asymptote of the graph of f if |
|
Definition
| f(x) approaches b as x approaches infinity or negative infinity. |
|
|
Term
| A rational function f has vertical asymptotes at |
|
Definition
| the zeros of the denominator |
|
|
Term
| A rational function f has one or no horizontal asymptote determined by comparing the degrees of N(x), the numerator, and D(x), the denominator. |
|
Definition
-If n < m, y = 0 is the horizontal asymptote.
-If n = m, the horizontal asymptote is the line y = an/bm.
-If n > m, the graph has no horizontal asymptotes. |
|
|
Term
| Shift f(x) = 3^x on unit to the left |
|
Definition
| g(x) = 3^(x+1) = f(x + 1) |
|
|
Term
| Shift the graph of f(x) = 3^x down two units |
|
Definition
| h(x) = 3^(x) - 2 = f(x) - 2 |
|
|
Term
| Reflect the graph of f(x) = 3^x in the x-axis |
|
Definition
|
|
Term
| Reflect the graph of f(x) = 3^x in the y-axis |
|
Definition
|
|
Term
| Formula for an exponential function that compounds n times a year |
|
Definition
A = P(1 + r/n)^nt
where A = amount, P = principle, r = interest rate, n = times per year, and t = time. |
|
|
Term
| Formula for an exponential function that compounds continuously |
|
Definition
A = Pe^rt
Where A = amount, P= principle, r = rate, and t = time. |
|
|
