1. Section 3.4 Basic Functions
Constant Function
Linear Function
Identity

2. Section 3.4 Basic Functions
Square Function
Quadratic
Cubic Function

3. Section 3.4 Basic Functions
Cube Root
Function
Absolute Value
Function

4. Section 3.4 Basic Functions
Rational Function
Square Root
Function

5. Section 3.4 Basic Functions
Greatest Integer Function

6. Section 3.4 Basic Functions
Continuous Functions
Is a function where the graph has no gaps, holes, or breaks…it can be drawn without stopping and lifting your pencil.
Discontinuous Functions
Is a function where the graph has gaps, holes, or breaks…it can not be drawn without stopping and lifting your pencil.

7. { Piecewise-Function for Find the following…
Find the inequality that is true for the value of x and plug the value into the function.
2. What is the domain of the function?
Use the individual domain restrictions to find the entire domain.

8. { Piecewise-Function for 3. Find all intercepts.
Y-intercept is when x = 0 or f(0).
The y-intercept is at ( 0, -1 ).
x-intercepts are when y = f(x) = 0. Take each individual function and set it equal to zero.
Not true.
The x-intercept is at ( 1, 0 ).
x = 1 is ok, but -1 violates domain.
Not possible, ½ is not in the domain.

9. { Piecewise-Function for 4. Graph the function.
Test all endpoints given in the domain restrictions.
Color coordinate the functions.
Test the -3 and -1 for the first function.
-2(-3) and (-1) + 1
6 + 1 = = 3
( -3, 7 ) ( -1, 3 )
Open point because of no equal to line.
Closed point because of equal to line.
Test the -1 for the third function, but it will be an open point. This is a quadratic function, so we will test points, 0, 1, 2, etc.
Test the -1 for the second function. This is a constant function with only x = -1, yields the point ( -1, 2 ).
(-1)2 – 1 = 0
( -1, 0 )
(1)2 – 1 = 0
( 1, 0 )
(3)2 – 1 = 0
( 3, 8 )
(0)2 – 1 = 0
( 0, -1 )
(2)2 – 1 = 0
( 2, 3 )

10. { Piecewise-Function for 5. Use the graph to determine the range.
Use your pencil as a horizontal line. Start at the lowest point on the graph and slide your pencil up. Identify all the y – coordinates that your touching.
6. Is f continuous on its domain? No

11. { 1. What is f(-2), f(5), and f(-1 )?
Piecewise-Function {
1. What is f(-2), f(5), and f(-1 )?
2. What is the domain of the function?

12. Piecewise-Function {
4. Graph the function.

13. { 3. Find all intercepts. x intercepts y intercept 5. Find the Range.
Piecewise-Function {
3. Find all intercepts.
x intercepts
y intercept
5. Find the Range.
6. Is f continuous on its domain? No