Graphing Rational Functions
Multiplying/Dividing Rational Expressions
Adding & Subtracting Rational Expressions
Solving Rational Equations
Random
100
f(x)=a(1/(x-h))+k
How does 'k' affect your graph?
Vertical Shift
100
What is the acronym to help solve this 1/(2x)-:3/2
K.C.F (Keep Change Flip)
100
When adding and subtracting fractions, what has to be the same between the two fractions?
It has to have the same denominator.
100
What is the first thing you need to find when solving rational equations?
LCD
100
What are Holes/Removable Discontinuity in the following example:
(x+2)/((x+2)(x-5))
Holes are factors that you cancel out, and visually, there will be a hole in the graph.
Hole x=-2
200
f(x)=a(1/(x-h))+k
How does 'h' affect your your graph?
It controls the horizontal shift.
200
What happens when you have 1/0 ?
Undefined
200
If given two fractions without a common denominator, what do we have to find between the two denominators?
Ex: 1/(3x)+1/6
LCD (Lowest Common Denominator)
200
Once you find the LCD, what do you do with it?
Multiply it to each fraction in the numerator
200
Find the remainder of (2x^3-5x^2-x+3)-:(x+3)
-93
300
f(x)=a(1/(x-h))+k
How does 'a' affect your graph?
It controls whether the graph compresses or stretches.
300
What are the excluded values/ "restrictions of x" of the following 1/((x+3)(x-5))
x!=-3,5
300
What would be the LCD here:
1/(4x)+3/(8)
LCD:8x
300
What is the LCD here:
1/(2x)+5/8=14/8
LCD: 8x
300
Find the remainder of the following (5x^3+x^2-7)-:(x+1)
-11
400
Whether on your notebook or drawing on your table with a marker, provide a rough sketch of what f(x)=1/x looks like.
400
Multiply the following and find the restrictions of x:
((x-2)/(x+5))((x+5)/4)
(x-2)/(4)
x!=-5
400
Simplify and find the restrictions of "x"
(x+3)/(x-5)+(7)/1
x!=5
(8(x-4))/(x-5)
400
Solve for x in the following rational equation:
1/(4x)-2/3=6/(2x)
x=-33/8
400
How do you find Horizontal and Vertical Asymptotes?
Example 1/(x-4)
H.A. if the degree of the denominator is bigger then y=0.
V.A. you set the denominator equal to zero and solve for x=4
500
Given: f(x)=1/(x-2)
What transformation occurred compared to the parent graph f(x)=1/x ?
There is a horizontal shift, two units to the right.
500
Find the restrictions of "x" and multiply
((x+2)/(x-1))(2+(x^2-9)/(x+3))
x+2
x!=1,-3
500
Simplify and find the Excluded Values (restricted x values)
1/(x-4)-(x+2)/(x^2-16)
x!=4,-4
2/((x+4)(x-4))
500
Solve for x for the rational equation.
7/(x^2-5x-24)+6/(x+3)=5/(x-8)
x=56
500
Emma and Jake are setting up for a concert event. If Emma works alone, she can set up all the sound equipment in 15 minutes. Jake, who has some experience with the equipment as well, could do the same job in 30 minutes on his own. If they work together to set up, how long will it take them to finish?
x=10