Ch. 1 – PREREQUISITES FOR CALCULUS 1.2 – Functions and Graphs

One input gives 2 outputs Functions Function = A set of ordered pairs that has each input (x) giving exactly one output (y) Ex: Domain = the set of all inputs (x) Range = the set of all outputs (y) X Y -2 3 4 8 32 7 5 X Y 5 3 4 8 32 -6 Function Not a function; One input gives 2 outputs

Functions Ex: A = πr2 . What is the range and domain? Domain = set of all r’s… Since r can’t be negative, domain is r≥0 Range = set of all A’s Since r≥0, we know A won’t be negative, so range is A≥0 Ex: When using a number line, there is no range, only domain. Write the following domains. The red line represents the domain. You must know both notations! 5 -5 All real numbers 5 -5 5 -5

Functions Ex: When using a number line, there is no range, only domain. Write the following domains. The red line represents the domain. 5 -5 5 -5 5 -5 5 -5

Domain and range of 2D Graphs Ex: Find the domains and ranges of each graphed function. Assume all real numbers unless the graph DOESN’T exist for a certain value Hint: Look for asymptotes, holes, and blank sections of the graph! Use parenthetical notation! Domain: Range:

Functions A function is even if it is symmetric about the y-axis (flip it over the y-axis and it’s the same!) f(-x) = f(x) A function is odd if it is symmetric about the origin (turn it upside-down and it’s the same!) f(-x) = -f(x) A graph symmetric about the x-axis is… …not a function!