1. Graphing Simple Rational Functions p 381
IF- 7d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

2. Essential Question

3. Definition A rational function is a function of the form
where p(x) and q(x) are polynomials. The most basic rational function with a variable expression in the denominator is

6. 0.01
– 0.01
0.001
– 0.001
0.0001 – 0+ 0-

7. The end behavior indicates that the graph of f(x) approaches, but does not cross, the
[x-axis / y-axis], so that the axis is an asymptote for the graph.

8. State the range of f(x) = 1/x .
The function takes on all real numbers except ………….. So the function’s range is as follows
As an inequality: y < ……….. or y > …………
.In set notation: {y | y ≠ ……… }
In interval notation: (– ∞, ……..) υ ( ……… , + ∞)

9. State the range of f(x) = 1/x .
The function takes on all real numbers except ……0…….. So the function’s range is as follows
As an inequality: y < …0…….. or y > …0………
.In set notation: {y | y ≠ …0… }
In interval notation: (– ∞, …0…..) υ ( …0… , + ∞)

10. Graphing Simple Rational Functions

11. Assignment 1.

12. Assignment 1. a = 3, h = 1, k = 2, b = 1 1 2 b – 1 + 1, 3(– 1) + 2
(0, – 1 )
1 + 1, 3(1) + 2
(2, 5 )

15. 1 1 1 1 1 2 2 2 2 2

16. Assignment 2.

17. Assignment 2. a = ½ , b =1, h = – 3, k = – 1 – 3 – 1 – 1– – 1 – 3.5 –2
– –2 1 1
– 2.5, 0

20. – 3
– 3
– 3
– 3
– 3
– 1
– 1
– 1
– 1
– 1

21. 3.

22. Assignment 3.
– 1

23. Assignment 3. a = ½, b = 1, h = – 1, k = – 3 – 1 – 3
(–1 – 1, –½(– 1 ) – 3 )
– 1
(–2, – 2.5 )
( 1 – 1, –½( 1 ) – 3 )
(0, –3.5 )

26. – 1
– 1
– 1
– 1
– 1
– 3
– 3
– 3
– 3
– 3