1. All About Functions
Chapter 2, Sections 1 & 6

2. Functions
A function is a relation in which the members of the domain do not repeat.
This means for every x-value there is only one y-value that corresponds to it
X-values can’t be repeated, y-values can
Vertical Line Test
If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph is a function.

3. Domain and Range
Recall that domain is the set of x values (independent variables) and the range is the set of y values (dependent variables)
To determine the domain: look at the x values.
On a graph, examine what happens as you go to the left and then as you go to the right.
To determine the range: look at the y values.
On a graph, examine what happens as you go up and then as you go down.

4. Does the graph represent a function? Name the domain and range.x y x y

5. Does the graph represent a function? Name the domain and range.x y x y

6. Does the graph represent a function? Name the domain and range.x y x y

7. One-to-one Functions
A special function where neither the x-values nor the y-values repeat.
Passes the vertical AND horizontal line test.

8. Does the graph represent a one-to-one function?x y x y

9. Does the graph represent a one-to-one function?x y x y

10. Function Notation Y=f(x)
f(x) is a notation to designate the function “f” evaluated at the variable “x”
Pronounced: f of x
To evaluate a function means to substitute a given value for the variable in a function

11. Examples: Find f(4) if f(x)=2x+3 Find g(-2) if g(x)=2x2-3x+5
Find h(a) if h(x)=9-7x+x3
Find h(2c) if h(x)=x2-x+7
Find f(a-1) if f(x)=x2-3

12. More examples: f(x)=5x-7 Find x if f(x)=2 Find x if f(x)=-9

13. Special Functions

14. Constant Function
y = 3
Y=b

15. Identity Function
y=x
y=x

16. Absolute Value Function
y=|x - 2|-1

17. Greatest Integer Function2 4 6 –2 –4 –6 x y
y=[x]
Y=[x] Also called the step function

18. Piecewise Function
2 or more functions combined together with restrictions on their domain
For example:

19. In Conclusion: Homework Exit Slip Page 7 in workbook
Problems 1-13
Exit Slip
In your own words, explain why the vertical line test works. 19