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

Essential Question

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

0.01 – 0.01 0.001 – 0.001 0.0001 – 0.0001 0+ 0-

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.

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 ( ……… , + ∞)

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… , + ∞)

Graphing Simple Rational Functions

Assignment 1.

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 )

1 1 1 1 1 2 2 2 2 2

Assignment 2.

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

– 3 – 3 – 3 – 3 – 3 – 1 – 1 – 1 – 1 – 1

3.

Assignment 3. – 1

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 )

– 1 – 1 – 1 – 1 – 1 – 3 – 3 – 3 – 3 – 3