1 / 16

Calculus Review Chapter 2

Calculus Review Chapter 2. Polynomial and Rational Functions Exponential Functions Logarithmic Functions. Polynomial Functions. Domain All real numbers The maximum number of turning points the graph of a polynomial of degree n can have? n-1

allegra-kirk
Download Presentation

Calculus Review Chapter 2

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. Calculus ReviewChapter 2 • Polynomial and Rational Functions • Exponential Functions • Logarithmic Functions

  2. Polynomial Functions • Domain • All real numbers • The maximum number of turning points the graph of a polynomial of degree n can have? • n-1 • Maximum number of x-intercepts the graph of a polynomial of degree n can have? • n

  3. Polynomials, cont. • So what is the maximum number of real solutions a polynomial equation of degree n can have? • n • The least number of x-intercepts the graph of a polynomial function of odd degree can have? • 1 • The least number of x-intercepts the graph of a polynomial function of even degree can have? • 0

  4. Polynomials, cont. 1.How many turning point are on the graph? 4 2. What is the minimum degree of a polynomial that could have the graph? 5

  5. Rational Functions • Given the rational function • f(x) = n(x)/d(x), where n(x) and d(x) are polynomials without common factors • What is the domain of f. • The set of all real number such that d(x) is not equal to 0. • If a is a real number such that d(a) = 0, then the line x = a is • A vertical asymptote of the graph of f.

  6. Rationals, cont. • There are three special cases to be aware of when finding horizontal asymptotes. • 1. If the highest power in the numerator and denominator is the same then • y= the quotient of the leading coefficients is a hor. Asymptote • 2. If the highest power is in the denominator then • y= 0 is a horizontal asymptote • 3. If the highest power is in the numerator then • There is no horizontal asymptote.

  7. Exponential Functions • The equation f(x) = b^x defines an exponential function. • b is called • the base • What is the domain of f? • All real numbers. • What is the range of f? • The set of all positive real numbers.

  8. Exponentials, cont. Basic properties of the graph of f(x)=b^x • All graphs will pass through which point? (0,1) • All graphs are Continuous curves, with no holes or jumps • The x-axis is A horizontal asymptote • If b>1, then b^x Increases as x increases • If 0<b<1, then b^x Decreases as x increases.

  9. Exponential Function properties • Exponent laws.

  10. Exponential Properties, cont.

  11. Interest Formulas • Compound Interest

  12. Interest Formulas, cont. • Continuous compound interest

  13. Logarithmic Functions • One-to-One Functions • A function f is said to be one-to-one if • Each range value corresponds to exactly one domain value. • Inverse of a Function • If f is one-to-one, then the inverse of f is the function formed • By interchanging the independent and dependent variables for f.

  14. Logarithmic Functions, cont. • The inverse of an exponential function is called • A logarithmic function. • For b>0 and b not equal to 1, • Is equivalent to

  15. Logarithmics, cont. • The log to the base b of x is • The exponent to which b must be raised to obtain x. • The domain of the logarithmic function is • The set of all positive real numbers • And the range is • The set of all real numbers

  16. Properties of Logarithmic Functions

More Related