Pre-Calculus: Functions

This chapter covered symmetries, basic equations of circles and parabolas, intercepts and line equation forms, some basic functions (linear, cubic, square root, reciprocal, step, absolute value, inverse, quadratic, etc), combinations of functions (including the composition of functions), the domains and ranges of functions, and direct and joint variation.

Areas that I will no doubt forget quickly and need to review are:

• Shifting (adding to the x side shifts up or down-fine; but the horizontal shifts are counterintuitive to me--f(x-c) shifts to the right)
• Reflections (to reflect over the x axis, negate it-fine; but to reflect on the y, you negate within the function f(-x).
• Stretches (a vertical stretch involves a number times the function that is greater than 1; a horizontal stretch is when the coefficient is between 1 and 0)
• Inverse functions involve switching the x and the y.
• The vertical line test tells if something is a function. The horizontal line test tells whether a function has an inverse. Only one-to-one functions can have inverses.