About Test 1

  • Covers chapters 1, 2, and part of 3 (3.1 and 3.2)
  • You may use pencil, pen, non-graphing calculator (not Wolfram Alpha)
  • 50 minutes on Monday
  • A chance to re-submit parts (for a lower grade) if you really flame out on a problem

Review / Study guide

  • Words, equations, graphs, tables: Know how to go from each of these to the other. So, given an equation, be able to plot several points on a graph from the function. Be able to identify independent variables and dependent variables.
  • Functions, domains, ranges, increasing / decreasing, rate of change is increasing / decreasing (concavity). A key part of functions is that for any allowed input there is one, and only *unique* output value.
  • Linear equations, equations, meaning of slope (rate of change of something), units of slope (y units divided by x units), y-intercept, x-intercept, figuring out equation from 2 points, average rate of change as the slope of a line connecting two points, perpendicular ($m_1m_2=-1$) / parallel ($m_1=m_2$) lines.
  • Quadratic functions, identifying "zeroes", vertex form, increasing / decreasing, identifying from a sketch or from the value of $a$ whether a parabola is concave up or concave down. The vertex is either the highest or lowest point on a parabola (depending on whether it opens down or up) and lies on the vertical line which is the axis of symmetry of the parabola.

  • Piecewise functions, how to graph them, specify a domain for different parts of the function.
  • Composite functions: how to evaluate $f(g(x))$ whether the functions are specified by a formula or a graph or a table.
  • Inverse functions: How to evaluate an inverse function (Interchange the roles of input and output). Coming up with a formula for an inverse function, based on the formula for the function. (E.g. solving $y(x)$ for $x$ to get $x(y)$.)