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 assignments 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 look at Lesson 3 (Continuity) to familiarize yourself with piecewise functions.

The f(x) function is quite similar to my examples I do in Lesson 1. 

The g(x) function is an example of a piecewise function.  The graph is composed of two pieces.  The first piece is for x values less than 5.  Check the domain of that piece keeping in mind that it is only interested in x values less than 5.  The second piece is just a horizontal line since y = 100 for all values of x greater than or equal to 10.  This means that g(x) was never defined for x values between 5 and 10! So, certainly, those values are excluded from the domain.

You may want to look at my message above giving you An Alternate Way to make Sign Diagrams.

I give you some more extensive tips on how to sketch a graph in my earlier message:

To sketch the graph of a piecewise function, merely graph each piece for the relevant x values.  For example, for the f(x) graph, sketch y=x^2 for all x values greater than or equal to 0.  Because that piece includes x=0, be sure to plot a dot at (0,0) to show that point is included.  The second piece is y=-x^2 for x-values less than 0.  Draw that graph.  To show that piece does not include 0, plot a hole at the end point (an open circle).  When x=0, y is also 0 at y=-x^2, so you would plot a hole at (0,0).  In this case, that hole is filled in by the dot you plotted at (0,0) for the first piece, so you end up with a continuous graph.  But, other piecewise functions may end up looking discontinuous, and that's when the holes and dots for the endpoints are vital.

Find the zeros of that function first.  There are two zeros. That gives you three sections (below the lower zero, between the two zeros, and above the higher zero).  Plot one or two points in each section.

The absolute value "flips" any part of a graph that would have been below the x-axis back above the x-axis, and causes sharp points (like a bouncing ball or gull wing) at the x-intercepts.  Consider drawing the graph of g(x) as though there were no absolute value signs first.  Then, flip the piece or pieces of graph that would have been below the x-axis above.

I discuss even and odd functions while doing Lesson 9, question 3(a).  The way the question is being asked, it seems to suggest that you are to decide if the function is even, odd or neither by merely looking at your sketch.  That is what I advocate, too.  If you want to be more thorough, you can confirm what you see with your own eyes, by computing f(-x), as I discuss in Lesson 9.

Be sure to read your graphs from left to right when identifying where the function is increasing.  Wherever the graph is rising from left to right, it is increasing.  Always list intervals of increasing or decreasing using round brackets ( ).  Which is to say, give open intervals, saying it is increasing up to, but not including the endpoint.

This seems to be a rather pointless exercise in transforming graphs.

You should know what a graph of sin(x) looks like already (if not, google it).  Be sure you are using radian angles rather than degrees on your x-axis.  Which is to say, show +/- pi/2, +/- pi, etc. rather than +/- 90 degrees, etc.

Adding or subtracting a number from x, slides the graph horizontally.  Adding slides left, subtracting slides right.  So, subtracting pi/2 from x, slides the graph pi/2 units to the right.

Adding or subtracting number from the entire function slides the graph vertically.  Adding slides the graph up, subtracting slides the graph down.  So, adding 3 to the whole function, slides the graph up 3 units.

You should know what a graph of e^x looks like already (if not, google it).  I also discuss it at the start of Lesson 8 in my book.  Again, they are subtracting 2 from x (sliding the graph to the right 2 units), then they add 3 (sliding up 3 units).

This question is even sillier.  Duh!  They told you it is an ellipse, so I think we know if it passes the vertical line test or not.  Google "graphing an ellipse" if you need assistance here.

These are called composite functions.  f o g is f(g(x)) or f at g at x, telling you to sub g(x) in place of x in the f function.  Conversely, g o f is g(f(x)).   When you sub one function into another, please simplify as much as you possibly can.  However, there really is not simplification possible here, adding to the pointlessness of this exercise.

Note the domain of f o g can be no better than the domain of the "inside" function (g in that case).  Establish the domain of g, then establish the domain of "f o g" as well and whichever domain is smaller is the domain of f o g.

Similarly, the domain of "g o f" is the smaller of the domains of f and the domain of "g o f".

Simply put, when you start with a function, say f, with a restricted domain, your domain can't get better, if you then sub f into g.  However, your domain can get worse.

Remember, you can only compute the log of a positive number.  You cannot compute the log of 0 or the log of a negative number, so logarithms restrict domains.  That will cause real problems for g o f since that has sinx stuck inside the logarithm.  Everywhere sinx is negative or 0 (look at your graph in question 3) will be exclude from the domain.  There will be an endless amount of intervals that are included and an endless amount that are excluded.  It should be sufficient to show them 3 or 4 consecutive intervals in the domain, and then use "..." on each end to emphasize it is endless.

I think that is a typo where they request f-inverse of y.  I assume they mean f-inverse of x.  Check with the prof about this!

I show you how to find the inverse of a function in Lesson 8 of my book (just after question 4 in the lecture, page 230).  I like to immediately have x and y change places, then proceed to isolate y. 

Again, you will change the logarithm into an exponential as part of finding the inverse function.

Remember, when stating the domain of a logarithm, you can only log positive numbers.  Find the zeros, and make a sign diagram, keeping in mind that you can't compute log of 0 or log of a negative.

What is this doing here???  They don't even discuss inverse trig until Math 1700.  I do discuss it in Lesson 1 of my Calculus 2 book which is posted as a free sample on my website.

Use the technique I illustrate on page 27 of my Calculus 2 book to make a right triangle.  In your case, inverse cosine x = theta, so that means cos(theta) = x.  Rewrite that as x/1 to make a right triangle with adjacent side x and hypotenuse 1.  Use Pythagorean Theorem to solve the opposite side.  You can now read sin(theta) off of the right triangle to answer the question.

This is similar to my Lesson 2, question 16(a).  Remember that my free samples at the top of this email include audio of me working through this question in my book.

This is very similar to my example at the start of Lesson 2.  Again, you may find the audio I provide helpful.