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Economics 214

Economics 214 . Lecture 9 Intro to Functions Continued. 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.

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Economics 214

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  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

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