Algebra 2 B- Lesson 3: Rational Functions and Their Graphs

You want to mix a 5% blue dye with a 20% blue dye to make a 12% blue dye. The function y=100(0.05)+x(0.2)/100+x gives the concentration y of the blue dye after you add x mL of the 20% dye to 100 mL of the 5% dye. How much of the 20% dye must you add to get a dye that is 12% concentrated?

87.5 mL

What is the graph of the rational function? y=-3x+5/-5x+2

Graph A

Find the horizontal asymptote of the graph of y=3x^6-7x+10/8x^5+9x+10

There is no horizontal asymptote

Describe the vertical asymptote(s) and hole(s) for the graph of y=(x+2)(x+4)/(x+4)(x+1)

asymptote: x=-1 and hole: x=-4

The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. The ship uses 30 barrels of oil in traveling 85 miles at 42 mi/h. How many barrels of oil are used when the ship travels 26 miles at 54 mi/h? Round your answer to the nearest tenth of a barrel, if necessary.

15.2 barrels.

The yearbook committee is distributing yearbooks to students by class. Each class has approximately the same number of students. The table shows the number of volunteers who helped to distribute the yearbooks to each of the four classes and the time needed to distribute the yearbooks. What function models the data?

nt=440

Find any points of discontinuity for the rational function y=(x+6)(x+2)(x+8)/(x+9)(x+7)

x=-9, x=-7

Suppose that y varies directly with x and inversely with z, and y=18 when x=15 and z=5. Write the equation that models the relationship. Then find y when x=21 and z=7.

y=6x/z; 18

Suppose that w and t vary inversely and that t=1/5 when w=4. Write a function that models the inverse variation, and find t when w=9.

t=4/5w; 4/45

This graph of a function is translation of y=4/x. what is an equation for the function?

4/x+6 +2

Graph the function y=13/6x

Graph C

Sketch the asymptotes, and graph the function y= 5/(x-2) +3

Graph C