1. Relations and Functions
Scavenger Hunt
Relations and Functions

2. “Function” A relationship in which each input value (x) has only one output value (y).
Domain
Input x 1 2 3 4 y 5 7 9 11
Range
Output

3. x 1 2 3 4 y -4 11 31 59
Are the following ordered pairs a function? (1,-4),(2,11), (3, 31), and (4,59)
YES!

4. “Function” A relationship in which each input value (x) has only one output value (y).
NOT a function

5. Exactly ONE “y” (range) for each value of “x”.
Functions
Range
Domain
Exactly ONE “y” (range) for each value of “x”.

6. Find the domain of f(x) = 2x + 1
Domain is all real numbers

7. Find the domain of
Domain is {x | x  4}

8. Find the domain of
Domain is {x | x  -5}

9. Domain is all real numbers
Find the domain of
Domain is all real numbers

10. Find the range of f(x) = 2x + 1
Range is all real numbers

11. Find the range of x y 2 4 6 -2 -4 -6 x y 2 4 -2 -4 -62 4 6 -2 -4 -6 x y 2 4 -2 -4 -6
Range is { y | y  0 }

12. Example: Graph each function f(x)= x+4 where the domain is {-2,-1,0,1,2,3}

13. Is this a graph of a function?
Vertical
Line
Test

14. Is this a graph of a function?

15. Is this a graph of a function?

16. Is this a graph of a function?

17. Is this a graph of a function?

18. Is this a graph of a function?

19. Is y = 3x – 4 a function?
Is x = y2 a function?

20. Is y = |x| a function?
YES
Is x = |y| a function?

21. Function Values The outputs are called function values.
Example: If we have f(8)=10 then 10 is the functional value and 8 would be the input

22. Find f(5) 12
Find f(-3) 4
Find f(0) 7

23. Find g(5) 7
Find g(-3) -9
Find g(0) -3

24. Linear Functions y=mx +b
The Triad Truck Rental Company charges $35 per day plus $0.21 per mile. Find the cost of renting a truck for a one day trip of 340 miles?

25. The Triad Truck Rental Company charges $35 per day plus $0.21 per mile. Find the cost of renting a truck for a one day trip of 340 miles?
f(x) = x
f(340) = (340)
f(340) = $

26. How can you tell whether or not a graph is a function?
Vertical line test
The vertical line can only cross the graph once in order for it to be a function

27. How can you tell whether or not a relation is a function
Only 1 domain goes to 1 range for lists
Only 1 x goes to 1 y value for (x,y)

28. What are the 3 ways a relations can be expressed?
Charts/ lists
Sets of ordered pairs/ graph
Formula/equation

29. How can you find the domain of a function?
The domain is the x values of a function.
Given ordered pairs (x,y) it’s the first entry
Given a list/chart the domain is always on the left
On a graph it is the x-axis