Asymptote??

1. Asymptote?? Start with the number one (1) and then divide it by two (2). Take that number that you got and divide that number by two (2). Continue this process several more times. What do you notice? Try doing the same thing but keeping it a fraction, what do you notice about the fraction?

2. Determining a Function one A relation is a function only if each input has exactly ____ output. If any input of a relation has more than one output, the relation is / is not a function. A relation is a function only if it passes the ______________. In other words, the line cannot hit the graph at more than ____ point anywhere. vertical line test one

3. -4 -1 2 3 -2 1 4 Determining a Function: Example 2 2. Tell whether or not the relation or the graph is a function: a) (-3,2), (4, -4), (2, -4), (-1,3) b) Input Output c) d) YES NO NO YES

4. What is a parent? a parent is the father or mother of someone or something; the roots of a thing; the place from which a thing is based The definition is no different in math when we relate the term to functions A parent function is a simple function that is the basis for all other functions of that type.

5. Parent Functions The parent function for the family of all: • Linear functions • Absolute value functions • Quadratic functions • Square root functions • Exponential functions • Logarithmic functions • Rational functions

6. The Linear Parent Function Enter it in Y= and graph it. y = mx + b

7. Quadratic Parent Function Enter it in Y= and graph it. The QPF is a U-shaped curve called a parabola .

8. Square Root Parent Function Enter it in Y= and graph it. The SRPF has a radical (the square root sign) in it.

9. The Absolute Value Parent Function Enter it in Y= and graph it. The AVPF looks like a V with its point on the origin.

10. Asymptote Is a line (can be vertical or horizontal) that the graph approaches, but never touches. We usually designate them with a dashed line, if not on the axis.

11. The Exponential Parent Function Enter it in Y= and graph it. The EPF has an asymptote along the x-axis

12. The Logarithmic Parent Function Enter it in Y= and graph it. The LPF has an asymptote along the y-axis

13. The Rational Parent Functionthe graph is called a hyperbola Enter it in Y= and graph it. The RPF has asymptotes along the x- and y-axis

14. Match-Up Summary Absolute Value Linear Square Root Quadratic

15. Are you my mother? Let's identify the parent fuctions for the following: Logarithmic Exponential Quadratic Linear Rational

16. Are you my father? Square Root Quadratic Absolute Value Linear

17. Domain and Range? DOMAIN: Is there any value that x CANNOT be? NO RANGE: Is there any value that y CANNOT be? NO DOMAIN: all real numbers or RANGE: all real numbers or

18. Domain and Range? DOMAIN: Is there any value that x CANNOT be? NO RANGE: Is there any value that y CANNOT be? YES- no negatives DOMAIN: all real numbers or RANGE:

19. Domain and Range? DOMAIN: Is there any value that x CANNOT be? YES- no negatives RANGE: Is there any value that y CANNOT be? YES- no negatives DOMAIN: RANGE:

20. Domain and Range? DOMAIN: Is there any value that x CANNOT be? NO RANGE: Is there any value that y CANNOT be? YES- no negatives and not zero DOMAIN: all real numbers or RANGE:

21. Domain and Range? DOMAIN: Is there any value that x CANNOT be? YES- no negatives and not zero RANGE: Is there any value that y CANNOT be? NO DOMAIN: RANGE: all real numbers or

22. Domain and Range? DOMAIN: Is there any value that x CANNOT be? NO RANGE: Is there any value that y CANNOT be? YES- no negatives DOMAIN: all real numbers or RANGE:

23. Domain and Range? DOMAIN: Is there any value that x CANNOT be? YES - not zero RANGE: Is there any value that y CANNOT be? YES - not zero all real numbers except 0 DOMAIN: or all real numbers except 0 RANGE: or