WorksheetsKey Features of Rational Functions
Total questions: 23
Worksheet time: 1hrs 14mins
What's the horizontal asymptote of the function?
y = 0
No horizontal asymptote
y = 2
y = 4
What's the horizontal asymptote of the function?
y = 0
No horizontal asymptote
y = 1/2
y = 1
What's the vertical asymptote of the function?
x = -9
x = 9
x = 3 , x = -3
x = 3
What's the vertical asymptote of the function?
x = 5
x = 0
x =5 , x = -5
x = 25
What's the vertical asymptote of the function?
x = -4, x = 1
x = 4, x = -1
x = -4, x = -1
x = 4, x = 1
What is the equation of the graph?
What are the x and y intercepts?
(4, 0) and (0, -4)
(-4, 0) and (0, -4)
(-4, 0) and (0, 4)
(0, 0) and (0, -4)
What are the coordinates of the y-intercept, if one exists.
(0, 0)
(0, 1)
(0, -1)
there isn't one
Find the x-intercept(s), if one exists.
(1, 0)
(-1, 0)
(1, 0), (-1, 0)
(0, 0), (1, 0)
How do you find the y-intercept?
replace all x-values with 0
replace all y-values with 0
set denominator equal to 0
compare the degrees of the numerator and denominator
How do you find the x-intercept?
replace all x-values with 0
replace the y-value with 0 or make the numerator equal 0
set denominator equal to 0
compare the degrees of the numerator and denominator
How do you determine the Horizontal Asymptote?
replace all x-values with 0
replace the y-value with 0 or make the numerator equal 0
set denominator equal to 0
compare the degrees of the numerator and denominator
How do you know if a factor in the denominator is a hole instead of a V.A. ?
It cancels out
it equals 0
you set the numerator equal to 0
you compare the degrees
When finding the H.A., if the numerator degree is one greater than the denominator degree, the answer is...
y = 0
Slant Asymptote
y =a / b
What's an H.A.?
When finding the H.A., if the numerator degree is equal to the denominator degree, the answer is...
y = 0
none
y =a / b
What's an H.A.?
Graph the function.
f(x)=x−4−x+1
What (if any) holes exist?
x=2
x=2 and x=3
x=-3
x=3
Find the coordinates of the hole.
(-3, -3)
(-3, 3)
(3, -3)
(3, 3)
What is the slant (Oblique) asymptote for the equation
f(x) = (x2 - 4x + 2)/(x + 3)
y = x -1
y = x -7
y = -7x + 23
y = -2x + 2
What type(s) of asymptotes does this function have? (Check all that apply.)
Vertical
Horizontal
Slant
What type(s) of asymptotes does this function have? (Check all that apply.)
Vertical
Horizontal
slant
