Mathematics 133 -- Intensive Calculus for Science 1

Information on Quiz 2

September 14, 2005

The second regular quiz of the semester will be given at the start of the class on Friday, September 16. On this quiz, there will be two or three questions similar to problems from section 1.3 and section 1.4. You should know the following material.

1. Obtaining new functions (and graphs) by
   • Vertical shifts: y - k = f(x) (shifts up if k > 0 and down if k < 0)
   • Horizontal shifts: y = f(x - h) (shifts left if h < 0 and right if h > 0)
   • Vertical stretching or shrinking: y = cf(x) (stretches if |c| > 1, shrinks if |c| < 1, plus a ``flip'' across the x-axis if c < 0)
2. Compositions f(g(x)) and g(f(x))
3. Inverse functions, and the ``horizontal line test'' for when a function has an inverse function
4. The natural logarithm function (inverse function of the exponential e^x)
5. Using natural logarithms to solve equations (including ones from ``word problems'' on half-lives, doubling times, etc.)

Good Review Problems:

1. Chapter 1, section 3: 3,5,6,7,14,22,27,41
2. Chapter 1, section 4: 17,23,29,35