2.1+Notes

An online presentation slideshow is available at http://docs.google.com/Present?docid=ddjh3n5r_30cwp685&fs=true. =2.1: Functions and Their Graphs=

Goal 2: Graph functions using a table of values.
//Relation//: a mapping, or pairing, of input values with output values.
 * Example: This example maps the input of a school name with the output of the corresponding school mascot.
 * **School Name** || **School Mascot** ||
 * Hillcrest High || Husky ||
 * Jordan High || Beetdigger ||
 * U of U || Ute ||
 * BYU || Cougar ||
 * U of Washington || Husky ||

//Domain//: the set of input values in a relation.
 * The domain of the school-mascot example is the set of schools, or in other words...
 * Domain = { BYU, Hillcrest High, Jordan High, U of U, UW }

//Range//: the set of output values in a relation.
 * The range of the school-mascot example is the set of mascots, or in other words...
 * Range = { Beetdigger, Cougar, Husky, Ute }
 * Note that we don't list Husky twice in the range.

//Function//: a relation in which there is exactly one output for every input.
 * Is the above relation, schools to mascots, a function?
 * Yes, the relation is a function. For each input, or school, there is exactly one output, or mascot.

//**Question: If we changed the above relation so the mascot was the input and the school name was the output, would this new relation be a function?**//

//Ordered Pairs//: A pair of numbers arranged in a specific order.
 * The most common form of ordered pairs seen in Algebra 2 are of the form (x,y), where x and y correspond to values on the x and y axes of a coordinate plane.

//Coordinate Plane//: A plane divided by two axes (x and y). The plane has four quadrants. Every point on the plane can be described by an ordered pair.

EXAMPLE 1: See http://www.uensd.org/class_pages/june22/rstewart/GeogebraNotes/FunctionOrNot.html for example problems.

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//Vertical Line Test//: a relation is a function if and only if no vertical line intersects the graph of the relation at more than one point.

EXAMPLE 2: THESE EXAMPLES WILL BE AVAILABLE AT A LATER TIME

//Independent Variable//: input variable in a relationship.
 * When looking at a graph, the independent variable is x.

//Dependent Variable//: output variable in a relationship. //Graph//: the collection of all points (x,y) whose coordinates are solutions of an equation.
 * When looking at a graph, the dependent variable is y.
 * Graphing an equation in two variables can be done using the following steps:**
 * 1) Construct a table of values.
 * 2) Graph enough solutions to recognize a pattern.
 * 3) Connect the points with a line or a curve.

EXAMPLE 3: THIS EXAMPLE COMING LATER

//Linear Function//: A function in the form math y=mx+b math where m and b are constants.
 * The graph of a linear function is a line.

//Function Notation//: Function notation uses the symbol f(x) for the dependent variable of a function. This means that we write math f(x)=mx+b math instead of math y=mx+b. math f(x) is read 'f of x' or 'the value of f at x'.

EXAMPLE 4: Decide whether the function is linear. Then evaluate the function when x = -2. math a) f(x)=-x^2-3x+5 math math b) g(x)=2x+6 math

EXAMPLE 5: A car has a 16 gallon gas tank. On a long highway trip, gas is used at a rate of about 2 gallons per hour. The gallons of gas //g// in the car's tank can be modeled by the equation math g=16-2t math where //t// is the time (in hours). a) Identify the domain and range of the function. Then graph the function.

b) At the end of the trip there are 2 gallons of gas left. How long was the trip?