The document provides examples of coordinate planes, functions, and evaluating functions at given values of x. It discusses identifying coordinates on a coordinate plane by moving right and down specified units. It also defines what makes a relation a function, which is that the x-values cannot repeat. Examples are given of evaluating functions by plugging values into the function equations and simplifying.
1. Module 4 Topic 1 Coordinate Planes/Midpoint/Relations and Functions
2. Example 1 Similar Problem: Follow these directions on a blank coordinate plane: Begin at the origin, move right 5 units, down 4 units. What are the coordinates of the ordered pair have you just graphed? Right 5 is going to be x = 5 Down 4 is going to be y = -4 (5, -4)
3. Example 2 For a function to exist, if you are looking at a set of ordered, none of the x-values can repeat. So if the x-values repeat at all then it is not a function.
4. Example 3 For a function to exist, if you are looking at a table, none of the x-values can repeat. So if the x-values repeat at all then it is not a function.
5. Example 4 Remember that if you have a vertical line it is not a function because it does not pass the vertical line test.
6. Example 5 Similar Problem: Let f(x) = 10x - 5.5. Find the value of f(3). 10x - 5.5 Plug in 3 for x and evaluate. 10(3) - 5.5 30 - 5.5 24.5
7. Example 6 Similar Problem: Let g(x) = x2 - 4x + 9. Find the value of g(-3) Plug in -3 for x. x2 - 4x + 9 (-3)2 - 4(-3) + 9 9 - (-12) + 9 9 + 12 + 9 30
