Functions in mathematics.

2. A function…….
• is a relation between a group of inputs and
outputs
• has each input related to exactly one output
• can be represented graphically or
symbolically

3. What types of functions were
investigated in Algebra?
• Linear
• Quadratic
• Cubic
• Exponential
• Absolute Value

4. • With a partner, using the
graph paper provided (no
graphing calculators yet),
sketch a graph for each of
the following functions:
-Linear, Quadratic,
Cubic, Exponential, and
Absolute Value

5. Linear Functions
What do linear functions look like
graphically?
*a line
How can you represent a linear function
symbolically?

6. Linear Functions–Let’s Investigate…..
What are some examples of linear functions?
On the graph paper provided, graph the function
y = ½ x – 4.
y = mx + b
Check your graph by graphing the function on
the graphing calculator.
Did you graph the function correctly?

7. Quadratic Functions
What do quadratic functions look like
graphically?
*a parabola
How can you represent a quadratic function
symbolically?
*y = ax2 + bx + c
*y = k(x – h)2 + g

8. Quadratic Functions–Let’s Investigate…..
What are some examples of quadratic functions?
On the graph paper provided, graph the function
y = -(x – 2)2 + 4.
Check your graph by graphing the function on
the graphing calculator.
Did you graph the function correctly?

9. Cubic Functions
What do cubic functions look like graphically?
*a curvy line
How can you represent a cubic function
symbolically?
* y = ax3 + bx2 + cx + d
* y = k(x – h)3 + g

10. Cubic Functions–Let’s Investigate…
What are some examples of cubic functions?
On the graph paper provided, graph the function
y = (x – 4)3 + 5.
Check your graph by graphing the function on
the graphing calculator.
Did you graph the function correctly?

11. Exponential Functions
What do exponential functions look like
graphically?
*a curved line that increases or decreases
rapidly
How can you represent an exponential
function symbolically?
* y = a(b)x + c

12. Exponential Functions-Let’s Investigate…
What are some examples of exponential
functions?
On the graph paper provided, graph the function
y = 3(2)x.
Check your graph by graphing the function on
the graphing calculator.
Did you graph the function correctly?

13. Absolute Value Functions
What do absolute value functions look like
graphically?
*a “V”
How can you represent an absolute value
function symbolically?
* y = a|x – b| +c

14. Absolute Value Functions-Let’s Investigate...
What are some examples of absolute value
functions?
On the graph paper provided, graph the function
y = |x + 3| - 6.
Check your graph by graphing the function on
the graphing calculator.
Did you graph the function correctly?

15. In Algebra II….
• we will investigate linear,
quadratic, cubic,
exponential, and absolute
value functions!
• we will take a look at
some new functions too!!
• we will have even more
fun graphing and
exploring functions than in
Algebra I!!!

16. Are you still confused?
• Take a look at the following website:
http://www.webgraphing.com/graphing_basic.jsp

17. Advanced Algebra II
Graphing Review
Sketch a graph for each of the following types of functions.
1. Linear Function
2. Quadratic Function
4. Exponential Function
5. Absolute Value Function
Name:__________________
Date: ___________HR:____
3. Cubic Function