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 y-value.
y = x²
x = y²
one of these is a function & one is not ...today we will learn how to tell which is which?!
Different ways to show a function:
A graph A mapping A set of ordered pairs
An equationA table
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)
3. f (2)
4. f(-3)
This means:Y= x2 + 1 when the x you are plugging in is less than zeroORY = x – 1 if the x you are plugging in is greater than or equal to zero
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 Square root Semi-Circle
Cubic LinearParabola
Y = x2
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 RestrictionsWhen 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
• 2. f(x) = √(2x + 1)•
• 3. f(x) = 3√(2x + 1)
• 4. f(x) = 4
x2 - 3
Examples: State the domain for each function.
5. f(x) = 1
3x + 5
6. f(x) = √(4 – x2)
Semi-Circle
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 PassState the Domain of Each:
•1. y = 7x – 4 • 3x2 – 6x
•2. y = √(2x – 11)
•3. y = 2x2 – 8
•4. y = √(36 – x2)