Calculus Review Chapter 2

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# Calculus Review Chapter 2 - PowerPoint PPT Presentation

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

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## Calculus Review Chapter 2

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Calculus ReviewChapter 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
• Maximum number of x-intercepts the graph of a polynomial of degree n can have?
• n
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
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

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.
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.
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.
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.

Interest Formulas
• Compound Interest
Interest Formulas, cont.
• Continuous compound interest
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.
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
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