1 / 17

Understanding Power and Polynomial Functions in Economics

Explore power functions with positive and negative exponents, along with polynomial functions and their roots. Learn about exponential functions and their properties in economic contexts.

akeem-powell
Télécharger la présentation

Understanding Power and Polynomial Functions in Economics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Economics 214 Lecture 9 Intro to Functions Continued

  2. Power function when p is positive odd integer • If k>0, then the function is monotonic and increasing. If k<0, then the function is monotonic and decreasing. • If p≠1 and k>0, the function is strictly concave for x<0 and strictly convex for x>0. • If p≠1 and k<0, the function is strictly convex for x<0 and strictly concave for x<0.

  3. Figure 2.14 Power Functions in Which the Exponent Is a Positive Odd Integer

  4. Power function with p negative integer • The function is non-monotonic • The function is not continuous and has a vertical asymptote at x=0.

  5. Power function with p negative integer

  6. Power function with p negative integer

  7. Figure 2.15 Power Functions in Which the Exponent Is a Negative Integer

  8. Polynomial Functions

  9. Polynomial Functions • The degree of the polynomial is the value taken by the highest exponent. • A linear function is polynomial of degree 1. • A polynomial of degree 2 is called a quadratic function. • A polynomial of degree 3 is called a cubic function.

  10. Roots of Polynomial Function

  11. 3 cases for roots of quadratic function • b2-4ac>0, two distinct roots. • b2-4ac=0, two equal roots • b2-4ac<0, two complex roots

  12. Quadratic example

  13. Plot of our Quadratic function

  14. Exponential Functions • The argument of an exponential function appears as an exponent. • Y=f(x)=kbx • k is a constant and b, called the base, is a positive number. • f(0)=kb0=k

  15. Exponential Functions

  16. Figure 2.16 Some Exponential Functions

  17. Exponential functions with k<0

More Related