- Find the domain and range of a function
- Recognize the four different ways to represent a function discussed in class
- Be able to express sets in number line, interval, and set description notations
- Understand and graph piecewise functions, including absolute value functions
(#3 cont.)
b. Give the domain of the function g.
c. Give the range of the function g.
d. Estimate the value of the y-intercept of the graph of g.
e. Estimate the value(s) of the x-intercepts of the graph of g.
4. Sketch the graph of a function that has no y-intercepts.
5. Explain why a function can have at most one y-intercept.
- Recognize and be able to graph all the special functions discussed in class
- Recognize and be able to graph transformations of graphs (vertical and/or horizontal shifts, reflections, and dilations/compressions)
- Combine two functions to get a new function by adding, subtracting, multiplying or dividing
- Take a graph with two functions f and g and sketch a graph of f+g, as demonstrated in class.
Some students have asked me, "What should I do to prepare for the exams?" Here are some tips for success on the midterm:
- Before the exam (as soon as possible!):
- Go over anything you missed on the quizzes and homework.
- Do lots of practice problems from the text.
- Make up practice problems and do them.
- Did I mention that practicing is a good idea?
- Do the practice exam (see 9/15 (3), below) under test conditions (in 50 minutes or less, with no notes and no calculator!). The actual exam may be shorter than the practice, so if you can complete the practice accurately in 50 minutes, you should not be in a hurry for the actual test.
- If you are unsure about anything at all, make time to come see me.
- Remember that understanding your notes is not enough; you must be good at doing problems you have not seen before, with no notes. So practice, practice, practice!
- During the exam:
- You do not have to do the problems in order. Skim through the test and do the easy ones first.
- Do not panic so much that you don't give yourself time to read the questions carefully. If you have followed the pre-exam advice, there shouldn't be any major surprises. If the phrasing of a question seems different from what you are used to, read the question slowly several times. If you are not sure what a question is asking, raise your hand.
- Be sure to give yourself enough time to check your answers. If an answer doesn't seem to make sense, but you don't have time to fix it, write a note explaining why you think there is a problem. Do everything you can to convince me you know the material.
9/19): There is a practice midterm you can download above. The solutions are now available above. Again, you are urged to complete the practice midterm under test conditions (no notes or calculators, in 50 minutes or less) in order to see clearly what you still have to work on. Then grade your test using the solutions. Please see me if there is anything in the solutions that you do not understand. The value of practice cannot be overemphasized. Practice makes perfect!!- Say in words what the limit of a function means
- Given a graph of a function f(x), determine the limit, the left-hand limit, and/or the right-hand limit of f(x) as x approaches a given number (no infinite limits).
