Rational F(x)'s

Horizontal/Slant Asymptotes

100

Find the Horizontal Asymptote of the following equations: 7/6x-2 and 2x+3/x^2+2x-8

Because the exponents in the denominator are larger than the exponents in the numerator, you know that the Horizontal Asymptote is y=0 because of Rule #2.

200

Find the Horizontal Asymptotes of this equation... 6x+1/12x+2

-The equation,6x+1/12x+2 will have an equal ratio of the y-intercept, because the top and the bottom exponents are equal, because of Rule #1.

300

Find the Horizontal Asymptote of the following equation, If there is no Horizontal asymptote, find the slant asmyptote: 3x^2+8x+7/3x+1

Because the exponent on the top (2) is larger than the exponent on the bottom (1), there is no horizontal asymptote. But there is a slant asymptote, which by solving with long division, and placing the numerator inside the "doghouse" you will find the slant asymptote to be: x+2.3 (or x+2 and 1/3) using long division you are able to find this answer.

400

What is the name of Maleficent's pet bird?

Diablo

500

Answer the following "true or false" questions. 1)You have more than one Slant Asymptote 2)You can have both a slant and a horizontal Asymptote 3)Rational Functions will sometimes Touch the Horizontal Asymptote

1)False, you can only have one. 2)False. Because the slant is simply an adjusted Horizontal Asymptote, you can not have both a horizontal and a slant. 3)True. the horizontal asymptote will sometimes be crossed by a point on the graph.

Vertical Asymptotes

100

Answer the following Questions: 1) What is the maximum number of Vertical Asymptotes possible? 2) How do you know by looking at a rational f(x) the number of vertical asymptotes?

1) The maximum is 2 2) The highest exponent in the denominator will tell you how many vertical asymptotes there are.

200

What is the real first and last names of the Marvel super hero, Hawkeye?

Clint Barton

300

Find the Vertical Asymptote of the following equation: 3x^2+8x+7/3x+1

The Vertical Asymptote of 3x^2+8x+7/3x+1 is -1/3, because you have to set the denominator equal to zero and solve for x, and you will end up with -1/3

400

Find the Vertical Asymptote of the following equations: 7/6x-2 and 6x+1/12x+2

-The Vertical Asymptote of 7/6x-2 is 1/3, because you need to set the denominator equal to zero, and when you solve you get 1/3. -The Vertical Asymptote of 6x+1/12x+2 is -1/6, because you need to set the denominator equal to zero and solve for x.

500

Solve for the vertical asymptotes of the following equation: (x^2-4)/(x^2-2x-3)

First you need to set the denominator equal to zero and then solve it by factoring, or Lopez approach (or Quadratic formula/completing the square), and you can find that the Vertical Asymptotes are: -1, and 3

X & Y Intercepts

100

Find the x and y-intercept of the equations: 7/6x-2 and 6x-1/12x+2

-There is no x-intercept of 7/6x-2, because when you set the numerator equal to zero, zero does not equal 7. -The x-intercept of 6x-1/12x+2 is 1/6, because you need to set the numerator equal to zero and solve for x. -The y-intercept of 7/6x-2 is -3.5, because when you when you use the formula plugging in zero for x, you end up dividing 7 by -2, the answer to that step is -3.5. -The y-intercept of 6x+1/12x+2 is 1/2, because when you plug in zero for x to solve for y, the answer that comes up as a fraction is 1/2.

200

Find the x-intercepts and y-intercept of the following equation: 3x^2+8x+7/3x+1

The two values of the x-intercept are x=-.58 and x=-2.07. You get these values by putting the numerator (3x^2+8x+7) into the Quadratic Formula, and solving the formula. When you end up solving for the positive and negative sides of the equation, the positive side of the equation will be x=-5.8 and the negative side of the equation will be x=-2.07. The y-intercept of the equation is 7 (7/1=7), because you plug in 0's for all the x's as the y intercept is when the x value is zero

300

What is Peter Parkers middle name?

Benjamin

Domain & Ranges/Tables

100

Find the Domain and Range of the following equation: 7/6x-2

-D: {all x values from negative infinity to positive infinity excluding 1/3 (the vertical asymptote)} -R: {all y values from negative infinity to positive infinity excluding zero (the horizontal asymptote)}

200

Show the Domain and Range of the following equation: 3x^2+8x+7/3x+1 (graph: http://i.imgur.com/bWcV845.png)

- D: {all x values from positive infinity to negative infinity excluding -1/3} -R: {all y values from positive infinity to negative infinity excluding all that land on x+2.3} - *the exclusions are based on the fact that the graph will never touch the vertical asymptote or the slant asymptote*

300

How do you find the table of any given rational Function?

Insert the function into the "y=" of your calculator, making sure to use parentheses, and then write down the points that are near the vertical asymptotes.

400

What is the Domain and Range of this graph? http://i.imgur.com/sHxrtbT.png (equation: x^2-4/x^2-2x-3)

D: {all x values from negative infinity to positive infinity excluding -1 and 3} (because the points will hit everything but the horizontal asymptotes R: {all y values from negative infinity to positive infinity} (because the graph actually goes through the Horizontal Asymptote, there is no point on the graph that the function will not touch)

500

What is Jesus Aguilar's favorite color? And why is that odd?

Green. He is Red/Green color blind

Real Life Example/Importance/Graphing

100

How can you find the Horizontal Asymptote of an equation?

You find the Horizontal Asymptote by taking a look at how many powers of x you have in the left corners of the equation. If you divide the top left value by the bottom left value, then there you have your HA! Ex: 6x-2/12x+2... Divide 6x by 12x and your HA is 1/2.

200

How do you graph a Rational Function?

insert the function into your calculator, graph the points closest to the vertical asymptotes, and then connect as you see on the picture of the graph in your calculator.

300

Find the Graph, Horizontal Asymptote, and Vertical Asymptote of the following word problem: "The ice cream shop has a deal going, if you buy one cone for $3, then additional cones are only $2.50 each. As you buy more and more cones (more and more lucky friends!), what is the average cost per cone?" -Explain the real life application of the Asymptotes of this graph in this word problem.

Link to Graph:http://i.imgur.com/kHepHbp.jpg Application of the Vertical Asymptote: -The cost of an ice cream cone will never be zero dollars, because the store will never charge that much for an Ice Cream Cone. The Vertical Asymptote will be zero and the graph never touches at that part of the graph, which shows that ice cream cones won't be priced at zero. Application of the Horizontal Asymptote: -The cost of each cone will never increase, because the set price of each cone is $2.50. 2.5 is the highest point that the price will be at(the Horizontal Asymptote).

400

What is a "Quokka"?

A small marsupial, similar to a wombat, but makes facial expressions similar to smiles.