Rational and Exponential Fucntions

Rational and Exponential Fucntions

1. Rational Function- a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.

2. Rational Functions-a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.

3. Horizontal & Vertical Asymptotes of Rational Functions-An asymptote is a line that the curve approaches but does not cross. A horizontal line is an asymptote only to the far left and the far right of the graph. "Far" left or "far" right is defined as anything past the vertical asymptotes or x-intercepts.

4. Exponential Function-almost exclusively used as a shortcut for the natural exponential function ex, where e is Euler's number, a number (approximately 2.718281828) such that the function ex is its own derivative.

5. Horizontal Asymptotes of Exponential Functions- y=0

6. End behavior of a graph with asymptotes- end behavior asymptotes model the behavior of the function at the left and right ends of the graph. The distance between the curve and the line approaches zero as we move out further and further out on the line.

7. Y-intercept of an exponential function- where the line of the graph crosses the y-axis, y=2^(x-1)

8. Initial amount for an exponential function- a in the formula is the initial amount for the exponential function

9. Exponential Growth- occurs when the growth rate of the value of a mathematical function is proportional to the function's current value.

10. Exponential Decay- A model for decay of a quantity for which the rate of decay is directly proportional to the amount present.

11. Growth Factor of an Exponential Function- the growth factor is b and the formula is b=(1+r)

12. Decay Factor of an Exponential Function- The decay factor is b and the formula is b=(1-r)

13. Compound Interest Formula- p(1+r/n)^nt P = principal amount (the initial amount you borrow or deposit) r = annual rate of interest (as a decimal) t = number of years the amount is deposited or borrowed for. A = amount of money accumulated after n years, including interest. n = number of times the interest is compounded per year

14. Continuous Compound- A=Pe^rt

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