Download 1.2A Notes

Bellwork
1. Write the equation of a line that passes through
(-2, 5) and is perpendicular to
4x – 3y = 10.
2. Write the equation of a line that passes through
(-1, 7) and is parallel to y = 3.
3. In 1991, there were 57 million cats as pets in
the US. By 1998, this number was 61 million.
Write a linear model for the number of cats as
pets. Then use the model to predict the number of
cats as pets in 2015.
Section 1.2
•Functions
What is a function?

A special relationship such that every
x-value is paired with only one yvalue.
one of these is a function
y = x²
& one is not ...today we
x = y²
will learn how to tell which
is which?!
Different ways to show a function:
A graph
A mapping
A table
An equation
A set of ordered
pairs
Determine if each is a function
of x.
1. 3x + 7y – 2 =
0
2. y = x(x – 10)
3. x = 4
4. x = y2
5. y = 10x + 12
6. x2 + y2 = 16
7. y = 4
8. y = √(x)
9. y = x2 – 3
10. y = l x l
How can you decide?
If you know the shape of the graph use VLT, if
not solve for y and see if every x value would be
paired with one y value.
Function Notation
What does f(3) mean?
What is the corresponding y value when x = 3?
Evaluating a Function.
Let f(x) = 1 – x2. Find each.
1. f(3)
2. f(2a)
3. f(x + 3)
Given that f(x) = 12x – 7,
which statement is true?
a. f(3) = 30
b. f(1/2) = 16
c. f(a) + f(1) = 12a + 5
d. f(a + 1) = 12a + 5
Answer:
Evaluate the Piecewise
function
Find each:
1. f(-1)
2. f(0)
This means:
Y= x2 + 1 when the x you are
plugging in is less than zero
OR
Y = x – 1 if the x you are
plugging in is greater than or
equal to zero
3. f (2)
4. f(-3)
Now use GUT
How to put in GUT:
Y1=(x2 + 1)/(x<0)
Y2=(x – 1)/(x>0)
Evaluate the Piecewise
Fucntion
Find each.
1. g(2)
2. g(-4)
3. g(1)
4. g(0)
5. g(-3)
6. g(3)
Now use GUT
How to put in GUT:
Y1=(x + 3)/(x<0)
Y2= (3)/(0<x and x
<2)
Y3=(2x – 1)/(x>2)
Evaluate with GUT:
g(10)
g(-7)
Special functions you should know:

Absolute value

Parabola
Y = x2

Square root

Semi-Circle

Linear

Cubic
Y=x
Y = x3
Domain of a Function and
Domain Restrictions
The domain of a function is all real
numbers unless the x value gives you a y
value that is undefined or imaginary.
Example: f(x) = 1/x
What value would make this problem
undefined?
Domain Restrictions
When you have a denominator, the
denominator can not be = 0!
When you have an even indexed radical,
the radicand must be > 0!
If there is an even indexed radical in the
denominator, then the radicand must be
> 0!
If you have a rational exponent remember
that this stands for a radical!
Examples: State the domain
for each function.
• 1. f(x) = 3x2 – 3
• 3. f(x) = 3√(2x + 1)
• 2. f(x) = √(2x + 1)
•
• 4. f(x) =
4
x2 - 3
Examples: State the domain for
each function.
5. f(x) =
1
3x + 5
SemiCircle
2
6. f(x) = √(4 – x )
Examples: State the domain for
each function.
• 7. g(x) = (3x+ 1)1/3
• 8. f(x) = 4x ½
•
• 9. f(x) = 3x
•
x2 – 2
•
•
Examples: State the domain for
each function.
• 10. g(x) = 5
•
√(x-1)
•
• 11. f(x) = 3x2/3
• 12. f(x) =
•
3
4x – 1
State the Domain for each
function
12. p(x) = 1
x2 + 5
13. f(x) = √(2x2 –
10x)
Give the domain for each.
1. f(x) =
x4
– 10
2. f(x) = 2x – 3
3x2 – 9x
3. f(x) =
3√(2x
+ 3)
4. f(x) = 2√(16 – x2)
5. f(x) =
4
√(x – 7)
6. f(x) = (2x + 5)1/4
Exit Pass
State the Domain of Each:
•1. y = 7x – 4
•
3x2 – 6x
•2. y = √(2x – 11)
•3. y = 2x2 – 8
•4. y = √(36 – x2)