Math 140 - Week 1 Notes

Wednesday, February 17

Today we started by reviewing fractions. You need to know how to add/subtract/multiply and divide fractions. To help remind you how to do that, I made this video:

We also reviewed the basic rules of algebra, and I posted this Algebra Rules - Cheat Sheet.

Friday, February 19

Today we practiced simplifying rational expressions by factoring, and then we talked about function notation and why it can be confusing. Here are the problems we did in class.

  1. Simplify \(\displaystyle \frac{x^2 + 5x + 6}{x^2 + 4x + 4}\).

  2. Simplify \(\displaystyle \frac{x^2 - 5x + 4}{1 - \frac{1}{x}}\).

  3. Simplify \(\displaystyle \frac{1}{x} - \frac{2}{x^2 + 2x}\).

  4. If \(f(x) = x^2\) and \(g(x) = x+5\), find \(f(g(4))\) and \(g(g(4))\).

  5. The quantity of gasoline \(Q\) sold by a gas station is a function of the price \(p\) that the owner sets. Here is a graph of the function \(Q = Q(p)\). Use the graph to find \(Q(3)\) and to solve \(Q(p) = 3000\) for \(p\).

  1. The function \(f(x) = \frac{1}{2}(x + \frac{2}{x})\) can be used to approximate \(\sqrt{2}\). Calculate \(f(2)\) and \(f(f(2))\).

  2. The number of large animals that can be supported by a square kilometer of land is a function \(N(m)\) that depends on the average mass (\(m\)) in kilograms of the animals. If \(N(50) = 5\), what does that mean in words?

  3. If \(C(p)\) is the amount of carbon monoxide in the air, measured in parts per million (ppm), as a function of the number of residents \(p\) in a town (measured in thousands of people). If the population of the town is growing so that \(p(t) = 10 + 0.1 t^2\) where \(t\) is the number of years from now, then find the formula for a function that will predict the amount of carbon monoxide in the air \(t\) years from now.