Formalizing Relations Functions After todays lesson you should
- Slides: 21
Formalizing Relations & Functions After today’s lesson, you should be able to: ØExplain the difference between a relation and a function ØIdentify whether a relation is a function ØIdentify the domain and range of a relation or a function ØEvaluate a function for specified
Are we related? Determine whether the following quantities are related. Justify your answers 1) Brother and sister 2) Step mom and step-son 3) Distance from work and gas used
Relations A ______is a set of ordered pairs, (x, y). The (age, height) ordered pairs below form a relation.
Domain and Range The _______ of a relation is the set of the first coordinates of the ordered pairs. The ______ is the set of second coordinates. List the values in order from least to greatest but
Relations Write the domain. {________ } Write the range {________ } How can you tell which is the domain 0 5 1 10 2 15 3 20
Graphing Write this. Relations relation as a set of ordered pairs. -2 {_________} 0 Graph the relation. 5 7 -3 6 12
Functions A _____is a relation that assigns exactly one y-value for every x-value. (x cannot have two different y x 0 1 2 3 y -6 -1 4 9
Functions Compare and contrast the definition of a relation and a function. Determine if each relation a function. t. If not, f(t) t is f(t) explain. -5 -5 -5 7 0 -5 2 -1 5 -5 2 4
Graphing Sketch a. Functions graph of this function. t 0 1 2 3 f(t) -6 -1 4 9
VERTICAL LINE TEST If the vertical line passes through more than one point of the graph, the relation ______ a function. Why? NOT A FUNCTION
Mapping Diagram A mapping diagram draws arrows from the domain of a function to its range. List the Domain and Range Domain Range Is this a function?
Exit Ticket Create a table of at least 4 points Write this relation as a set of ordered pairs Sketch the graph of your relation Is this a function? Justify your answer.
Mapping Diagram Draw a mapping diagram for the following relation? Is it a function? Domain Range
5 -4 & 5 -5 Evaluating Functions To evaluate a function for a specified domain To determine if a rule is that of a function To find the range of a function for a specified domain
“Functions Rule” !! A function rule is an equation that describes a function. A function rule as an input-output machine.
Example: If y = 3 x + 4 Another way to write the function y = 3 x + 4 is f(x) = 3 x + 4. x INPUTf(x) OUTPUT This is read as “_______”. Other notation may be g(x), h(x), etc.
Function Junction what’s Your Function!!
Evaluating Functions a) Suppose f(x) = -3 x + 10. Evaluate for x = 6 b) Suppose f(x) = -3 x + 10. Evaluate f(0). c) Suppose y = -3 x + 10. Evaluate for x = -1
Find domain given range Given y = 3 x – 2, what value of x that would make y = 7 What value of x would make y = -17?
What’s the range for my domain? If given the domain, you can find the range of a function. Example: Evaluate f(a) = -3 a + 5 for the domain {-3, 1, 4}. What is the range?
Exit Ticket The cost of a long distance telephone call, c, is function of the time spent talking. The rule c(t) = 0. 09 t describes the cost after talking t minutes. What does the domain and range represent in this problem? Domain Range Find c(45). What is the input value? What is the output value?
