Algebra 1 4.5 Writing a Function Rule
4.6 Formalizing Relations and Functions
Name _____________________________
Example 1: Write a function rule that represents each situation
a) The total cost C of p pounds of coffee if each pound costs $3.57
b) The amount of y of your allowance if the amount of your allowance is $4 more than twice your friends
allowance x
c) Y is 4 less than the product of 5 and x
d) 3.6 more than the quotient of p and 4 is q
---------------------------------------------------------------------------------------------------------------------------------------------------------------Example 2: Write a function rule for the area of a triangle with a base of 5 cm greater than 6 times its height.
What is the area of the triangle when its height is 8 cm?
Example 3: Tom is 3 years older than 2 times his sister’s age.
Write a function rule that represents Tom’s age as a function of his sisters age s.
How old is tom if his sister is 3?
---------------------------------------------------------------------------------------------------------------------------------------------------------------Relation- a pairing of numbers in one set; represented by a set of ordered pairs (x,y).
Domain- set of x-values
Range- set of y-values
Function- a relation in which each domain value is mapped to only one range value (x-values cannot repeat).
Example 4: Identify the domain and range of each relation. Represent the relations with a mapping diagram. Is the
relation a function?
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a) {(
)}
b) {( ) ( ) ( ) ( )}
---------------------------------------------------------------------------------------------------------------------------------------------------------------Vertical Line TestIs the relation shown below a function? Use a vertical line test.
Notice that two of the dashed vertical lines pass through just one point on the graph.
However, one of the dashed vertical lines passes through three points.
The function is not a relation
Example 5:
Example 6:
---------------------------------------------------------------------------------------------------------------------------------------------------------------{
}.
{
}.
Example 7: the domain of ( )
Example 8: the domain of ( )
What is the range?
What is the range?
---------------------------------------------------------------------------------------------------------------------------------------------------------------Example 9: What is f(8) for the function f(x)=2x+3?
Example 10: What is f(-3) for the function f(x)=2x+3?
---------------------------------------------------------------------------------------------------------------------------------------------------------------Classwork/Homework:
Write a function rule that represents each sentence.
1. t is 4 more than the product of 7 and s.
2. The ratio of a to 5 equals b.
3. 8 fewer than p times 3 equals x.
4. y is half of x plus 10.
5. k equals the sum of h and 23.
6. 15 minus twice a equals b.
7. m equals 5 times n increased by 6.
8. 17 decreased by three times d equals c.
9. 5 more than the product of 6 and n is 17.
10. d is 8 less than the quotient of b and 4.
11. Twelve cans of peaches are placed into each box. Write a function rule
for the number of boxes needed for c cans. How many boxes are needed for 1440 cans?
12. Tara plans to rent a car for the weekend. The cost to rent the car is $45 plus $0.15 for each mile she
drives. Write a function rule for the total cost of the rental. How much is the rental if she travels 500
miles?
13. A plumber charges $60 for a service call plus $55 for each hour she works. Write a function rule for
the total bill for a plumbing job. What is the total bill for a job that takes the plumber 3 hours of
work?
14. Tickets to a concert cost $45 per ticket plus a $10 processing fee for each order. Write a function rule
for the total cost of ordering tickets. What is the total cost to order 6 tickets?
--------------------------------------------------------------------------------------------------------------------------------------------------Identify the domain and range of each relation. Use a mapping diagram to determine whether the relation is a
function.
15. {(2, 3), (4, 6), (1, 5), (2, 5), (0, 5)}
16. {(3, 4), (5, 4), (7, 4), (8, 4), (10, 4)}
Use the vertical line test to determine whether the relation is a function.
17.
18.
19
20.
--------------------------------------------------------------------------------------------------------------------------------------------------------------21. The domain of ( )
What is the range?
{
}.
22. The domain of ( )
What is the range?
{
}.
---------------------------------------------------------------------------------------------------------------------------------------------------------------23. What is f(-2) for the function f(x)=2x+3?
24. What is f(3) for the function f(x)=2x+3?