1. functions graphically
Now, on to more practice
with Section 1.3b:
Today, we analyze
functions graphically
and explore piecewise
functions…

2. Quality Practice Problems
Graph the given function, then answer the following questions: 8
1. On what intervals is the function
increasing or decreasing?
Inc: [ 2, )
Dec: (– , 2 ] 8
2. Is the func. even, odd, or neither?
Neither
3. What are the extrema of the func.?
Min. of 0 at x = 2
4. Does the graph relate to one of
the 12 basic functions? If so, how?
The squaring func.,
shifted right 2
5. What is the domain and range of
the function?
D: (– , ) 8 8
R: [ 0, ) 8

3. Quality Practice Problems
Graph the given function, then answer the following questions:
1. On what intervals is the function
increasing or decreasing? 8
Dec: [ – 4, )
2. Is the func. even, odd, or neither?
Neither
3. What are the extrema of the func.?
Max. of 0 at x = – 4
The square root func.,
shifted left 4, reflected
across x-axis
4. Does the graph relate to one of
the 12 basic functions? If so, how?
5. What is the domain and range of
the function?
D: [ – 4, ) 8
R: ( – , 0 ] 8

4. Quality Practice Problems
Graph the given function, then answer the following questions: 8
1. On what intervals is the function
increasing or decreasing?
Inc: ( – , –1 ]
Dec: [ –1, ) 8
2. Is the func. even, odd, or neither?
Neither
3. What are the extrema of the func.?
Max. of 5 at x = –1
The abs. val. function,
reflected across x-axis,
shifted left 1, up 5
4. Does the graph relate to one of
the 12 basic functions? If so, how?
5. What is the domain and range of
the function?
D: (– , ) 8 8
R: (– , 5 ] 8

5. So, what are these functions
with “smart parts?”
Piecewise Functions!!!

6. x if x > 0 f(x) = –x if x < 0
Which of the twelve basic functions has the following
piecewise definition over separate intervals of its domain?
x if x > 0
f(x) =
–x if x < 0
This is the absolute value function!!!

7. 8 8 8 Function is continuous! D: (– , ) R: [0, )
Sketch the given function (without using your calculator!), list
any points of discontinuity, and state the domain and range of
the function.
Function is continuous!
D: (– , ) 8 8
R: [0, ) 8

8. Point of discontinuity
Sketch the given function (without using your calculator!), list
any points of discontinuity, and state the domain and range of
the function.
Point of discontinuity
at x = 0
D: (– , ) 8 8
R: (– , 0 ] U ( 1, ) 8 8

9. Point of discontinuity
Sketch the given function (without using your calculator!), list
any points of discontinuity, and state the domain and range of
the function.
Point of discontinuity
at x = 0 8 8
D: (– , )
R: (– , ) 8 8

10. 8 8 8 Function is continuous! D: (– , ) R: [ 0, )
Sketch the given function (without using your calculator!), list
any points of discontinuity, and state the domain and range of
the function.
Function is continuous!
D: (– , ) 8 8
R: [ 0, ) 8

11. Point of discontinuity
Sketch the given function (without using your calculator!), list
any points of discontinuity, and state the domain and range of
the function.
Point of discontinuity
at x = 2, 3, 4, 5,… 8 8
D: (– , )
R: [ 0, ) 8

12. Whiteboard Problems
Graph the given function, then answer the following questions:
1. On what intervals is the function
increasing or decreasing?
Inc: [ 0, ) 8
Dec: (– , 0 ] 8
2. Is the func. even, odd, or neither?
Even
3. What are the extrema of the func.?
Min. of 3 at x = 0
4. Does the graph relate to one of
the 12 basic functions? If so, how?
The abs. val. function,
shifted up 3
5. What is the domain and range of
the function?
D: (– , ) 8 8
R: [ 3, ) 8

13. Whiteboard Problems
Graph the given function, then answer the following questions:
1. On what intervals is the function
increasing or decreasing?
Inc: (– , ) 8 8
2. Is the func. even, odd, or neither?
Neither
3. What are the extrema of the func.?
No extrema
4. Does the graph relate to one of
the 12 basic functions? If so, how?
The exp. function,
shifted up 2
5. What is the domain and range of
the function?
D: (– , ) 8 8
R: ( 2, ) 8