Math 141: Chapter 1 Review - Functions, Graphs, and Equations in Two Variables

MATH 141 Chapter 1: Graphs and Functions (Review)

Distance Formula 1.1 Example: Find distance between (-1,4) and (-4,-2). Answer: 6.71

Midpoint Formula Example: Find the midpoint from P1(-5,5) to P2(-3,1). Answer: (-4,3)

y (x, y) r (h, k) x 1.2 Equations in two variables – Example: Circle Equations The standard form of an equation of a circle with radius r and center (h, k) is: The Unit Circle equation is:

1.3 Definition of a Function

Theorem: Vertical Line Test A set of points in the xy - plane is the graph of a function if and only if a vertical line intersects the graph in at most one point.

y x Not a function.

y x Function.

Summary Important Facts About Functions • For each x in the domain of f, there is exactly one image f(x) in the range; however, an element in the range can result from more than one x in the domain. • f is the symbol that we use to denote the function. It is symbolic of the equation that we use to get from an x in the domain to f(x) in the range. • If y = f(x), then x is called the independent variable or argument of f, and y is called the dependent variable or the value of f at x.

A function f is even if for every number x in its domain the number -x is also in its domain and f(-x) = f(x) A function f is odd if for every number x in its domain the number -x is also in its domain and f(-x) = - f(x) 1.4 Properties of Functions: Even and Odd Functions

Determine whether each graph given is an even function, an odd function, or a function that is neither even nor odd.

Where is the function increasing?

Where is the function decreasing?

Where is the function constant?

Local Maxima and Minima Local Max

Local Min

Average rate of change of a Function

From 0 to 1

1.5 Library of Functions (Famous Functions)

Piecewise-defined Functions: Example:

1.6 Graphing Functions:

On Calculator:

Math 141: Chapter 1 Review - Functions, Graphs, and Equations in Two Variables