Don't have my book or audio?  You can download a free sample of my book and audio lectures containing Lessons 1 and  2:

Did you read my tips on how to study and learn Math 1500?  If not, here is a link to those important suggestions:

These are tips for the first assignment in the Distance/Online Math 1500 course, but I strongly recommend that you do this assignment as homework even if you are taking the classroom lecture section of the course.  These assignments are very good (and challenging) practice.  The first assignment is a great way to build and review key skills that will be helpful for this course.

Here is a link to the actual assignment, in case you don't have it:

Note that you need to study Lesson 1 (Skills Review) and Lesson 2 (Limits) from my Intro Calculus book to prepare for this assignment.  I also recommend that you study Lesson 4 (Definition of Derivative) as the algebra skills that are taught in that lesson will assist you with question 1 below.

This question uses the skills that I teach in Lesson 4.  It is actually the definition of derivative but without doing the limit as h goes to 0.  I suggest you study that lesson to learn the necessary skills (such as simplifying Triple Deckers).  Do not use limits, of course, but make sure you have simplified to the point of factoring h out of the top and canceling with the h below.

This question involves graphing parabolas and completing the square.  I do discuss this a little bit in my Calculus for Management book.  It is included in the free sample posted on my website:

The section in the link above dealing with parabolas begins on page 17.

A function is one-to-one if it passes both the vertical line test (a vertical line can never pass through more than one point on the graph), proving it is a function, and the horizontal line test (a horizontal line can never pass through more than one point on the graph), proving it is one-to-one (that one value of x has only one value of y on the graph.

Sketch the graph of the parabola, and it is obvious that it fails the horizontal line test.  So you restrict the domain to make it one-to-one.  The most logical thing to do is to restrict the domain to all the x values from the vertex and larger.

Make sure you have read the Logs and Exponentials section of Lesson 1 in my book (starts on page 23).

Use a log law to combine the left side into one logarithm, then convert the log to an exponential.

Very similar to some of my examples in Lesson 1.

Hint: If e^x is t, then e^2x is t-squared.

To sketch each piece of this function, merely plot 2 or 3 points for the domain of each piece and connect the dots.  For example, graph y= x^2 - 2 for the region of (-infinity, -1) by plotting 3 points in that region.  For sure, one of those points should be the endpoint at -1.  However, since that region is up to but not including the endpoint, plot a "hole" at that location rather than a dot.  Which is to say, there will be a hole at (-1, -1).

The second piece is defined solely at x=-1, so merely plot a dot at (-1, 3) to represent that piece.

Once you have graphed all four pieces of this function, it is a simple matter to read off the solutions for all the limits, similar to what I do with my opening example in Lesson 2 of my book.

This is a good run-through of limits.  Study Lesson 2 thoroughly to prepare for this question.  This is the most important question on this assignment, in my opinion.  Many of these limits could appear on your final exam.

Standard limit problem.

Challenging.  Uses my factoring tip that I introduce just before I do question 1 in Lesson 2.  But you will have to use polynomial long division to factor this properly.  The second factor will be a trinomial (quadratic) if you do it right.