Factoring Practicex2 16

x3 + 27

25x2 + 15x2 10x + 24

16x2 -36

27x3 - 8(x 4)(x + 4)(x + 3)(x2 - 3x + 9)5(5x2 + 3)(x 6)(x 4)4(2x 3)(2x + 3)(3x 2)(9x2 +6x + 4)

5.2 Graphing Simple Rational Functionsp. 310What is the general form of a rational function?What does the h & k tell you?What does the graph of a hyperbola look like?What does the graph of ax+b/cx+d tell you?What information does the domain & range tell you?

Rational FunctionA function of the form

where p(x) & q(x) are polynomials and q(x)0.

HyperbolaA type of rational function.Has 1 vertical asymptote and 1 horizontal asymptote.Has 2 parts called branches. (blue parts) They are symmetrical.Well discuss 2 different forms.x=0y=0

Hyperbola (continued)One form:

Has 2 asymptotes: x=h (vert.) and y=k (horiz.)

Graph 2 points on either side of the vertical asymptote.

Draw the branches.

Hyperbola (continued)Second form:

Vertical asymptote: Set the denominator equal to 0 and solve for x.

Horizontal asymptote:

Graph 2 points on either side of the vertical asymptote. Draw the 2 branches.

SOLUTIONSTEP 1Draw the asymptotes x = 0 and y = 0.Plot points to the left and to the right of the vertical asymptote, such as (3, 2), (2, 3), (2, 3), and (3, 2).STEP 2

Draw the branches of the hyperbola so that they pass through the plotted points and approach the asymptotes.STEP 3Both graphs lie in the first and third quadrants and have the same asymptotes, domain, and range.

Ex: Graph State the domain & range.Vertical Asymptote: x=1Horizontal Asymptote: y=2x y-5 1.5-2 12 54 3Domain: all real #s except 1.Range: all real #s except 2.Left of vert. asymp.Right of vert. asymp.

Ex: GraphState domain & range.Vertical asymptote:3x+3=0 (set denominator =0) 3x=-3 x= -1Horizontal Asymptote:

x y-3 .83-2 1.330 -.672 0Domain: All real #s except -1.Range: All real #s except 1/3.

A 3-D printer builds up layers of material to make three dimensional models. Each deposited layer bonds to the layer below it. A company decides to make small display models of engine components using a 3-D printer. The printer costs $24,000. The material for each model costs $300.3-D Modeling

Graph the function. Use the graph to estimate how many models must be printed for the average cost per model to fall to $700. What happens to the average cost as more models are printed?SOLUTIONSTEP 1Write a function. Let c be the average cost and m be the number of models printed.

STEP 2STEP 3Interpret the graph. As more models are printed, the average cost per model approaches $300.

Graph the function. State the domain and range.SOLUTION

What is the general form of a rational function?

What does the h & k tell you?Asymptotes are x = h, y = kWhat does the graph of a hyperbola look like?Two symmetrical branches in opposite quadrants.What does the graph of ax+b/cx+d tell you?cx+d = 0 is the vertical asymptote and y = a/c is the horizontal asymptoteWhat information does the domain & range tell you?Domain tells what numbers can be used for x and the range is the y numbers when put into the equation.

Assignmentp. 313, 6-8, 14-20, 28-31