Rational & Exponential Functions

Rational & Exponential Functions

1. Rational Function

   • A rational function is any function which can be defined by a rational fraction.

2. Continuous Compounding

   • The process of earning interest on top of interest. The interest is earned constantly, and immediately begins earning interest on itself.

3. Horizontal and Vertical Asymptotes of Rational Funtions

   • The x-axis is a horizontal asymptote. The horizontal line y = b is a horizontal asymptote of the graph of y = f(x). The y-axis is a vertical asymptote. The vertical line x = a is a vertical asymptote of the graph of y = f(x).

4. Exponential Function

   • A mathematical function in which an independent variable appears in one of the exponents. g(x) = 2x, where the base is the fixed number, and the power is the variable.

5. Horizontal Asymptotes of Exponential Functions

   • The equation of the horizontal asymptote of the graph of is y = 0, which is the x-axis. The graph is never parallel to the y-axis, but moves away from it at a steady pace.

6. End behavior of a graph with asymptotes

   • End behavior is useful to examine the trend in the function value as the value of x gets larger and larger in magnitude. It helps to tell us how does f(x) behave as the value of x increases to positive infinity or decrease to negative infinity;; Asymptotic behavior of graph of a function involves limits, since limits are the situations where a function approaches a value. A vertical asymptote will usually exist whenever the function doesn’t exist. Basically, there are two types of asymptote, Horizontal and Vertical.

7. Y-intercept of an exponential function

   • The parameter a is called the function's y-intercept.

8. Initial amount for an exponential function 76. Exponential growth function

   • The change that occurs when an original amount is increased by a consistent rate over a period of time. A constant rate of growth applied to a continuously growing base over a period of time.

9. Decay factor of an exponential function

   • When a > 0 and 0 < b < 1, the function models decay. b is called the decay factor.

10. Growth factor of an exponential function

    • When a > 0 and b > 1, the function models growth. b is called the growth factor.

11. Compound Interest Formula

    • A= P(1+r/n) ^nt

12. Exponential decay function

    • An original amount is reduced by a consistent rate over a period of time. In exponential decay, the total value decreases but the proportion that leaves remains constant over time.

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