1. 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.

2. 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:

3. 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:

4. 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.

5. 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.

6. 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

7. 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.

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

9. 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

10. 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

11. 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

12. 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

13. 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

14. Classwork odd Homework even.
Text Book pgs exercises 8-31
pgs exercises 7-46