CHAPTER 2: FUNCTIONS,EQUATIONS, AND GRAPHS2.1 Relations and Graphs
RELATIONS A relation is a set of pairs of input and output values. There are four ways to represent relations
EXAMPLE: REPRESENTINGRELATIONS The monthly average water temperature of the Gulf of Mexico in Key West, Florida varies during the year. In January, the average water temperature is 69°F, in February, 70°F, in March, 75°F and in April, 78°F. What is one way to represent this relation?
DEFINITIONS The domain of a relation is the set of inputs, also called the x-coordinates, of the ordered pairs. The range is the set of outputs, also called the y- coordinates, of the ordered pairs.
FUNCTIONS A function is a relation in which each element of the domain corresponds to exactly one element of the range. When using a mapping diagram to represent a relation, a function has only one arrow from each element of the domain. Example:
THE VERTICAL LINE TEST The vertical line test is used to test whether a graph represents a function. The vertical line test states that if any vertical line passes through more than one point on the graph of a relation, then the relation is not a function.
EXAMPLE: USE THE VERTICALLINE TEST. WHICH GRAPH(S)REPRESENTS A FUNCTION?
FUNCTIONS A function rule is an equation that represents an output value in terms of an input value. We write a function rule in function notation.
EXAMPLE: USING FUNCTIONNOTATION For f ( x ) = −2 x, + 5 what is the output for 1 the inputs: −3,0,& 4
EXAMPLE: USING FUNCTIONNOTATION For f ( x ) = −4 x + 1 ,what is the output for the inputs: −2,0,5
EXAMPLE: Tickets to a concert are available online for $35 each plus a handling fee of $2.50. The total cost is a function of the number of tickets bought. What function rule models the cost of the concert tickets? Evaluate the function for 4 tickets.
EXAMPLE You are buying bottles of a sports drink for a softball team. Each bottle costs $1.19. What function rule models the cost of a purchase. Evaluate the function for 15 bottles.