Welcome 2015-16 BC Calculus Students! You should have been given a
summer work packet to prepare you for our journey into the study of
calculus this fall. If you have not received your packet, or want
another copy, you can download it from the course folder on the website.
Past students have found this review to be very helpful upon
undertaking the study of calculus, and I'm sure you will, too!
Use this forum to post questions and discuss solutions regarding the
summer packet. Look to offer help to those who ask and post your
questions when you have them. There is only one rule on this forum:
ALWAYS RESPECT EACH OTHER! You can also refer to the discussions from previous summer work packets - just scroll down.
Some reminders:
1. the packet is due the first day of class for
a significant grade
2. your original work should be on separate paper
and done without a calculator except when specified
3. solutions
(without work) are posted in the course folder online
4. the list of helpful links is also posted in the course
folder.
**Follow on Twitter: @GrovesBCcalc**
Good luck! See you in September! ~Coach Wilson
I'm going over my packet to check for questions I've skipped along the way and #13 on the back of Week 1 continues to stump me. I can get a GCF but I'm not sure how to use the quadratic formula at that point. I'm also unsure how we know where the function is undefined. I tried to use the answers sheet but I can't even comprehend how that answer relates. Any advice you can give? -Claire Westerlund
ReplyDeleteHint: the gcf is -1/4x^(-1/3). The remaining polynomial factors into two binomials with rational exponents on the variable. To determine domain restrictions, ask yourself, "Is there a division by zero, or a negative radicand of an even root, or a nonpositive value in a logarithm (the Big 3 of domain issues)?"
DeleteReviewing unsolved problems, I'm still having trouble with the domain and range problems of week one. I want to ask if there is a different method besides finding the domain of the inverse to find the range, and specifically about number 9. Is the domain ONLY determined by the root in the numerator as opposed to the denominator in this case? I ask the inverse thing because I only get to the simplification after squaring the inverse on 9 before getting stuck.
ReplyDeleteFirst, the idea of determining a function's domain is EXTREMELY important! A function is useless if we do not know for what values it is defined. That said, we want the largest set of input values possible, so we will assume that the domain is the set of all real numbers. Then, we look for values that cause undefined outputs, such as division by zero, negative values of even roots, and nonpositive values within logarithms.
DeleteNow, for range (actually called the co domain in higher mathematics) the easiest method is to picture the graph of the function. This is where your knowledge of parent function shapes is vital.
For #2 on the second part of week 2.How does one solve a system of equations that includes an absolute value. I've tried using many online sources but there doesn't seem to be any that could help me with this specific question.
ReplyDeleteI would rewrite the equation without absolute values if I were me. Recall that |x| = x when x >0 and |x| = -x when x<0.
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