1. Sam Miner Department of Mathematics Dartmouth College
Math 3, Fall 2015
Sam Miner
Department of Mathematics
Dartmouth College
Class 2 - 9/18/2015

2. A domain problem Let f(x) = √x, and g(x) = 4 – x^2. What is the domain
of f °g(x)?
{x | |x| ≥ 2 }
{x | |x| ≤ 2}
{x | x > 2}
{x | x < 2}
As 4-x^2 and is not defined for we have that is not defined for 4-x^2.
This reduces to x^2 or . The domain is thus all other values.
Class 2 - 9/18/2015

3. Even and odd Suppose f is odd and g is even. Then fg is Odd Even
Odd and even
Neither
What are the definitions? Can a function be both even and odd? Neither even nor odd?
Class 2 - 9/18/2015

4. Nomenclature Let f(x) = (x^2 + 2x – 3) / (1-√x). Then f is
a polynomial
a rational function
a trigonometric function
an algebraic function
What do each of these terms mean? Why the distinction between rational and algebraic?
Class 2 - 9/18/2015

5. Even, Odd, Both, or Neither?
Paired exercise: 2 students one solver, one listener. One problem each switching roles. The solver talks through and explains the solution to the problem. The listener follows the exposition and asks questions to clarify the answer as best they can. The listener should prompt but not help (yet) – call on me for help if you get stuck.
BE KIND!
Use phrases like
I don’t understand X
Why is Y true?
I think we need to check Z.
Class 2 - 9/18/2015

6. Even and odd functions
Is f(x) = 2x^5 – x^3 even, odd, both, or neither?
Same pair – do this problem together. Make sure either one can present a solution.
Class 2 - 9/18/2015

7. Domain and range
Randomize pairs (find a new partner you don’t know). Same technique – if you went first last time, go second (if both 1st or 2nd, flip coin).
Find the domain and range of the two functions pictured above.
Class 2 - 9/18/2015

8. Domain and range
Find the domain and range of the function f(x) = 3 - √(2-x).
Consider the function g(x) = 4/(3-x). Are there any values which are not in the domain of g? What about the range?
Same pair – do this problem together. Make sure either one can present a solution.
Class 2 - 9/18/2015