1. 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.

2. Section 1.2 Functions

3. 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?!

4. Different ways to show a function: A graph A mapping A set of ordered pairs An equationA table

5. Determine if each is a function of x. 1. 3x + 7y – 2 = 0 2. y = x(x – 10) 3. x = 4 4. x = y 2 5. y = 10x + 12 6. x 2 + y 2 = 16 7. y = 4 8. y = √(x) 9. y = x 2 – 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.

6. Function Notation What does f(3) mean? What is the corresponding y value when x = 3?

7. Evaluating a Function. Let f(x) = 1 – x 2. Find each. 1. f(3) 2. f(2a) 3. f(x + 3)

8. 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:

9. Evaluate the Piecewise function Find each: 1. f(-1) 2. f(0) 3. f (2) 4. f(-3) This means: Y= x 2 + 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

10. Now use GUT How to put in GUT: Y1=(x 2 + 1)/(x<0) Y2=(x – 1)/(x>0)

11. Evaluate the Piecewise Fucntion Find each. 1. g(2) 2. g(-4) 3. g(1) 4. g(0) 5. g(-3) 6. g(3)

12. 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)

13. Special functions you should know: Absolute value Square root Semi-Circle Cubic Linear Parabola Y = x 2 Y = x Y = x 3

14. 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?

15. 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!

16. Examples: State the domain for each function. 1. f(x) = 3x 2 – 3 2. f(x) = √(2x + 1) 3. f(x) = 3 √(2x + 1) 4. f(x) = 4 x 2 - 3

17. Examples: State the domain for each function. 5. f(x) = 1 3x + 5 6. f(x) = √(4 – x 2 ) Semi- Circle

18. Examples: State the domain for each function. 7. g(x) = (3x+ 1) 1/3 8. f(x) = 4x ½ 9. f(x) = 3x x 2 – 2

19. Examples: State the domain for each function. 10. g(x) = 5 √(x-1) 11. f(x) = 3x 2/3 12. f(x) = 3 4x – 1

20. State the Domain for each function 12. p(x) = 1 x 2 + 5 13. f(x) = √(2x 2 – 10x)

21. Give the domain for each. 1. f(x) = x 4 – 10 2. f(x) = 2x – 3 3x 2 – 9x 3. f(x) = 3 √(2x + 3) 4. f(x) = 2 √(16 – x 2 ) 5. f(x) = 4 √(x – 7) 6. f(x) = (2x + 5) 1/4

22. Exit Pass State the Domain of Each: 1. y = 7x – 4 3x 2 – 6x 2. y = √(2x – 11) 3. y = 2x 2 – 8 4. y = √(36 – x 2 )