1. Pre-Cal Chapter 1 Functions and Graphs Section 1-2

2. Definitions • Domain(aka Input, Independent Variable): then x values of a given relation and function. • Range(aka Output, Dependent Variable): the y values that come from the relation and function. • Mapping: Showing the elements of the domain onto the elements of the range.

3. Definitions Cont. • Implied Domain: the domain of the algebraic expression. • Relevant Domain: the domain that we use that fits a certain situation with a model(ie volume). • Removable Discontinuity: this is a discontinuity in the graph that can be patched by redifining f(a) so as to plug the hole. • Jump Discontinuity: this not a removable discontinuity because there is more than just a hole at (a), this makes the gap impossible to plug with a single point.

4. Definitions Cont. • Infinite Discontinuity: a graph that has asymptotes in it, and these are definitely not removable. • Increasing: a function is increasing if, for any 2 points in the interval, a positive change in x results in a positive change in f(x). • Decreasing: a function is decreasing if, for any 2 points in the interval, a positive change in x results in a negative change in f(x). • Constant: a function is constant if, for any 2 points in the interval, a positive change in x results in no change in f(x).

5. Definitions Cont. • Bounded Below: a function is bounded below if it has a lower bound that it never gets below. • Bounded Above: a function is bounded above if it has an upper bound that it never gets above. • Bounded on an Interval: when you restrict the domain to a specific interval that we want to consider.

6. Definitions Cont. • Local Maximum: the range value of a function that has the greatest value of the graph in a given interval. • Absolute Maximum: the range value of a function that has the greatest value for the entire graph. • Local Minimum: the range value of a function that has the least value of the graph in a give interval. • Absolute Minimum: the range value of a function that has the least value of the graph for the entire graph. • Relative Extrema: the local maximums and minimums of a graph are also referred to using the term relative extrema.

7. Review Words • Even Function: highest exponent on variable is an even number. • Odd Function: highest exponent on variable is an odd number. • Horizontal Asymptotes: have the equation of y = b where b is some number value. • Vertical Asymptotes: have the equation of x = a where a is some number value.

8. Vertical Asymptotes • Remember, your vertical asymptotes are found by finding the values of x that make the denominator zero in functions equation. Where you have vertical asymptotes, this means that your graph is going off to infinity.

9. Horizontal Asymptotes • You can have no horizontal asymptote, a horizontal asymptote at y=0, or a horizontal asymptote at y=# • You have NO Horizontal Asymptote when the degree(highest exponent) in the numerator is bigger than the degree(highest exponent) in the denominator. • Your Horizontal Asymptote is y = 0 when the degree(highest exponent) in the numerator is smaller that the degree(highest exponent) in the denominator. • When your degrees are the same in the numerator and denominator your Horizontal Asymptote is found by dividing the coefficient in front of the variable with the highest exponent from the numerator by the coefficient in front of the variable with the highest exponent in the denominator.

10. Examples

11. Homework • Pg. 98-99(2-28even; 42-62even)