Operations with Rational Functions
Analyze Graphs of Rational Functions
Solving Rational Equations
Vocabulary
100
Simplify:
(5x+15)/(x+3)
5
100
What is the Vertical Asymptote of
f(x) =(2x - 3)/(x - 4)?
x = 4
100
(a-8)/a = 3/(a+5)
a=-4, 10
100
What is the difference between a closed and open circle?
What is a closed circle being included on a graph and an open circle not being included in a graph?
200
(a^2 + 7a + 12)/(a^2 - 9) * (a - 3)/(a+ 3)
(a + 4)/(a - 3)
200
What is the Horizontal Asymptote of the function:
f(x) = (2x - 3)/(x - 4)?
y = 2
200
Solve:
(x -2)/(x - 1) = x + 2
x = 0
200
How do you find the x and y intercepts?
What is plugging in zero for x to find the y-intercept and setting the numerator equal to zero to find the x-intercept?
300
(c^2 - c - 12)/(c^2 + 4c + 3) : (c^2 - 6c + 8)/(c^2 + 5c + 4)
(c + 4)/(c - 2)
300
Define the hole in the function:
f(x) = (x^2 - 64)/(x^2 + 9x + 8)?
(-8, 16/7)
300
3/(2n) + 1/n^2=(n-2)/(2n^2)
n = -2
300
What is a hole and how do you find it?
What is the point on the graph that is undefined and is the number that sets the denominator to zero in the cancelled expression?
400
(x)/(x-4) - (6x)/(x - 5)
(-5x^2 + 19x)/((x - 4)(x - 5))
400
Identify the x and y intercepts in the function:
g(x) = (x - 4)/(2x - 8)
(0, 1/2) and (4, 0)
400
3/k - 1/2 = 12/k
k=-18
400
How do you find the Horizontal and Vertical Asymptote?
What is the degree for the Horizontal Asymptote and the number that sets the denominator equal to zero for the Vertical Asymptote?
500
Solve:
(3x + 6)/(x + 5) : (x + 2)/(x^2 - 25)
What is 3(x - 5)?
500
Graph the function
f(x) = (2x - 3)/(x - 4)
500
Solve:
(x^2 - 4)/(x + 3) + (x - 2)/(x + 3) = 2
x = 4
500
What is the Domain and Range?
What is the x values included in the graph for domain and y values included in the graph for range?