MATH 150 FINAL - REVIEW

MAJOR TOPICS:

This is a list of the basic material presented in MATH 150. It may not encompass all of the material or types of question included on the final, but it does provide a compendium of the basic material needed to succeed on the final.

FUNCTIONS:

Composition

Domain

Range

Computing inverse functions

Functions used in modeling

Graphing

Average rate of change

Examples:

Find the range and domain of the above functions:

Graph the above functions.

Graph the above functions with x replaced by: x-3, 2x, 2-x.

Find the composition of:

(For what values of x are the above compositions defined?)

Find the inverse of the following functions: and

Find the average rate of change for each of the above functions between x=5 and x=9.

Basic Functions: (Know what the graph looks like; know how to establish the domain and range)

Log, ln

Exponential functions

Basic rational functions

Functions with a discontinuity

List the domain, range, and graph of the following functions:

Polynomials:

Find the zeros

Behavior of the graph near zero

Graphing

Number of Zeros

Behavior for values of x far from the origin

Graph the following polynomials. (Pay attention to the behavior of the polynomials near the zeros and for values of x far from the origin).

, ,

Find the zeros of:

Rational Functions:

Domain

Vertical and horizontal asymptotes

Determination of the range

Slant Asymptotes

Graphing

Expressing in the form R(X)=N(X)/D(X) = P(X)+Q(x)/D(x)

For each of the following rational functions: state the domain, range, asymptotes and sketch the graph of the function.

Express the following rational functions in the form P(X) + Q(x)/D(x)

Quadratic Functions:

Representing in standard form

Vertex (min/max values)

Intercepts

Plot

Focus of the parabola

Represent each of the quadratics in standard form. Find the intercepts, vertex, and focus of each and graph the parabola.

Equations:

Linear

Linear Systems

With logs

With exponentials

Nonlinear Systems

Rational

Conics: Ellipse, Hyperbola, Circle:

Find the equation for given geometric information

Given the equation, derive geometric information (semi-major/minor axis, asymptotes, foci, graph)

For each of the following find the graph, identify the foci, asymptotes (where appropriate), & vertices.

,

Find the equations of the ellipse with: Foci = (0,5) and (0,-5) and major axis of length 12

Find the equations of the hyperbola with: Foci = (0,8) and (0,-8) and asymptotes .

Exponentials and Logs:

Properties of

Transforming equation involving log to exponentials

Graphing

Use in Modeling: Radioactive decay (Half-life), Compound interest, population growth, etc.

Solving equations which contain terms involving these functions

Problems:

  1. Find the present value of $100,000 if interest is paid at a rate of 9% per year for 5 years.
  2. The population of a specie of birds is model as

, where t is measured in years. Find the initial population of the bird. What happens to the population as time gets large. Draw a sketch of n(t).

Find:

Set up equations to solve a given problem (WORD PROBLEMS):

Page 647 (Text) problems: 38, 39, 40, 41

Parametric Equations:

Sketch the Curve:

,

Inequalities:

Solve:

Complex Numbers:

Find the real and imaginary parts of each of the following:

,,,

Limits:

,

Algebraic Expressions: Radicals, exponentiation laws, adding/multiplying rational expressions.

Simplify: