PowerPoint Part I

1. Algebraic Functions
Caron White
EDU 290

2. What are Algebraic
Functions?
A function that involves only
algebraic operations, like,
addition, subtraction,
multiplication, and division as
well as fractional or rational
exponents.
y= is now f(x)=

3. Function Input
Number inserted into
the function.
f(x)=x+7
f(3)=3+7
This is known as Domain
(x).

4. Function Output
Number “spit out” of
function.
The outcome of an input.
f(3)=3+7=10
This is known as Range
(y).

5. Functions With Same
Output
Different inputs
can have equal
outputs.
This IS a
function.

6. Is it a Function?
One input
has two
outputs.
This is NOT a
function.

7. Ordered Pairs
Points on a
graph.
Can be pulled
from a table.
{(2,6),(3,5),
(5,7),(7,9)}

8. Vertical Line Test
Only one
point
crosses.
If two
points=>not
a function.

9. Linear Algebraic
Functions
A function that can be
graphically represented in
the Cartesian coordinate
plane by a straight line.
f(x)=mx+b

10. Solving for Linear
Functions
27x+9y=18 solve for y
-27x from both sides
9y=-27x+18
/9 on both sides
y=-3x+2

11. Tables for Linear
Functions
Input values
for x
f(x)=-3x+2

12. Graphing Linear
Functions
f(x)=mx+b
b is the y-intercept
m is the slope
x is any value
(input)

13. Graphing Linear
Functions Continued
f(x)=-3x+2
Graph
points from
table

14. Is This a Linear
Function?
14x-28y=7 solve for y
-14x from both sides
-28y=-14x+7
/-28 on both sides
y=(1/2)x-(1/4)
Yes! Fractions can be constants!

15. Is This a Linear
Function?
−𝟗𝒙 𝟐
+3y=12 solve for y
+𝟗𝒙 𝟐
to both sides
3y=9𝒙 𝟐
+12
/3 on both sides
y=3𝒙 𝟐
+4

16. Continuation…
y=3𝒙 𝟐+4
No! This is a
Quadratic
function!
Quadratics are
our next section.

17. Citations
 Slide 2 Citation:
Algebraic Functions: Definition & Examples. (n.d.).
Retrieved from
http://study.com/academy/lesson/algebraic-function-
definition-examples.html
 Slide 9 Citation:
Linear Function. (n.d.). Retrieved from
http://www.icoachmath.com/math_dictionary/Linear_Funct
ion.html