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)