Chapters

1. Domain of the function.
2.Intersections with the x-axis and y-axis.
3. Asymptotes.
4.Increases and decreases.
5. Maxima and minima.
6.Concavity and convexity.
7. Inflection points.
Domain
x-intercepts
y-intercept
Asymptotes
Increases and Decreases
Minimum
Maximum
Concavity and Convexity
Inflection Points
Graph the Function

To represent a function graphically, calculate the points or intervals in the function where it changes its behavior. To do so, find the following mathematical characteristics:

1. Domain of the function.

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2.Intersections with the x-axis and y-axis.

3. Asymptotes.

4.Increases and decreases.

5. Maxima and minima.

6.Concavity and convexity.

7. Inflection points.

Representation of a Function Example

Domain

x-intercepts

y-intercept

Asymptotes

Horizontal asymptote

There are no vertical or oblique asymptotes.

Increases and Decreases

Minimum

Maximum

Concavity and Convexity

Inflection Points

Graph the Function

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Graphing Functions

1. Domain of the function.

2.Intersections with the x-axis and y-axis.

3. Asymptotes.

4.Increases and decreases.

5. Maxima and minima.

6.Concavity and convexity.

7. Inflection points.

Representation of a Function Example

Domain

x-intercepts

y-intercept

Asymptotes

Increases and Decreases

Minimum

Maximum

Concavity and Convexity

Inflection Points

Graph the Function

Theory

Exponent Rules

Composition of Functions

Constant Functions

Convergent and Divergent Sequences

Even and Odd Functions

Exponential Function

Graphing rational function IV

Graphing Parabolas

Arithmetic Sequence

Mean Value Theorem

Rolle’s Theorem

Intervals of Increase and Decrease

Periodic Functions

Concave and Convex Functions

Graphing rational function I

Graphing rational function III

Inflection Points

Increasing and Decreasing Functions

Geometric Sequence Problems

Piecewise Functions

Trigonometric Functions

Arithmetic Sequence Problems

Linear Function

Domain of a Function

Maxima, Minima and Inflection Points

Graphing exponential function II

Linear Functions Worksheet

Monotone Sequence

Radical Functions

Function

Geometric Sequence

x- and y-Intercepts

Bounded Sequence

Graphing rational function 8

L’Hôpital’s Rule

Graphing polynomial function I

Graphing exponential function I

Absolute and Relative Maxima and Minima

Maxima and Minima

Types of Functions

Asymptotes

Coordinates in the Plane

Optimization

nth Term

Graphing rational function V

Limit of a Sequence

Inverse Function

Graphing rational function II

Graphing logarithmic function

Graphing polynomial function II

Quadratic Function

Absolute Value Function

Rational Functions

Sequences

Bounded Functions

Logarithmic Functions

Properties of Limits

Formulas

Sequence Formulas

Exercises