Relations and Functions. Direct Variation. What you’ll learn To graph relations. To Identify functions. To write and interpret direct variations equations. Vocabulary Relation, domain, range , function, vertical line test, function rule, function notation, independent variable, dependent variable.

Take a note: Relation: And can be represented in different ways: Is a set of pairs of input and output values. And can be represented in different ways: Ordered pairs: (-3,4), (3,-1), (4,-1),(4,3) Mapping Diagram: -3 3 4 4 -1 3 Table of Values: x y -3 4 3 -1 Graph:

Problem 1:When skydivers jump out of an airplane, they experience free fall. The relation Shows the time and the height of the skydiver during the free fall. How can you represent this relation in four different ways Ordered pairs: {(0,10,000),(4,9744),(8,8976),(12,7696),(16,5904)} Table of values: Time(s) 4 8 12 16 Height(ft) 10000 9744 8976 7696 5904 4 8 12 16 10000 9744 8976 7696 5904 Mapping:

Remember: Input: Output: Vertical Line test: Domain: Range: Function: Independent variable Dependent variable States that if a vertical line test passes through more then one point of the graph of a relation, then the relation is NOT a function. Is the set of inputs, also called x-coordinates of the ordered pairs. Is the set of outputs, also called y-coordinates of the ordered pairs. Is a relation in which each element of the domain corresponds with exactly one element of the range.

Answer: Answer: Your turn: Is this relation a function? Why? What is the domain and the range in problem1? Answer: Is this relation a function? Why? Answer: Yes, because each element of the domain have exactly the element of the range.

NO YES YES Your turn: Answer NO YES YES Problem 2: Using the vertical line test. Which graph(s) represent functions. NO YES YES Your turn: Answer NO YES YES

A function rule is an equation that represents an output in terms of an input value. Examples: Reads as “f of x” Reads as “f of 1” Independent value The independent value x is the DOMAIN of the function. Dependent value The dependent value f(x) represents the RANGE of the function.

Problem 3: Using a function notation Answer: Your turn: Answer:

For 4 tickets Problem 4:Writing and Evaluating a Function. 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? Let t the number of tickets Let C(t) the total cost For 4 tickets Your turn: You are buying bottles of sports drink for a softball team. Each bottle costs $1.19.What is the function rule? Evaluate the function for 15 bottles? Answer

Your turn Problem 5: Identifying Direct Variation from tables Note: For each function, determine whether y varies directly to x. if so, what is the constant variation and the function rule? Your turn x y 1 2 3 6 4 8 x Y 1 4 2 8 3 11 x y 3 -21 2 -14 1 -7 x y 2 5 3 7 6 13 Answer

For each function, determine whether y varies Problem 6:Identifying direct variations from equations For each function, determine whether y varies directly with x. If so, what is the constant variation? Answer Since you can write the equation in the form y=kx and y varies directly with x. constant variation Is No, because you can not write y=kx. Answer

Problem 7: Using proportion to solve a direct variation. Suppose y varies directly with x and y=9 when x=-15. What is y when x=21. Your turn: Suppose y varies directly with x and y=15 when x=3. What is y when x=12. Answer 60

Problem 8: Using direct variation to solve a problem. A salesperson’s commission varies directly with sales.For $1000 in sales, the commission is $85. What is the commission for $2300. Your turn: The number o calories varies directly with the mass of cheese. If 50g of cheese contain 200 calories, how many calories are in 70g of cheese? Answer

Classwork odd Homework even. Text Book pgs. 65-66 exercises 8-31 pgs. 71-72 exercises 7-46