WorksheetsMastering Rational Functions
Total questions: 15
Worksheet time: 8mins
What is a rational function?
A rational function is the product of two polynomials.
A rational function is a single polynomial.
A rational function is a constant value.
A rational function is the ratio of two polynomials.
Identify the rational function from the following: f(x) = (2x + 3)/(x - 1) or g(x) = 5x + 2.
f(x) = (2x + 3)/(x - 1)
m(x) = 7/(x - 3)
k(x) = 4x^2 + 5
h(x) = (3x + 1)/(x + 2)
Graph the rational function f(x) = (x^2 - 1)/(x + 1). What are the asymptotes?
No vertical asymptote; horizontal asymptote at y = 1.
Vertical asymptote at x = -1; no horizontal asymptote.
Vertical asymptote at x = 1; horizontal asymptote at y = 0.
Vertical asymptote at x = 0; no horizontal asymptote.
Simplify the rational expression (3x^2 - 12)/(3x).
(3x - 12)/(3x)
(x^2 - 4)/3
(x - 2)/x
(x - 2)(x + 2)/x
Perform the operation: (2/x) + (3/x^2).
(2/x^2) + (3/x)
(2/x) - (3/x^2)
(2x + 3)/x^2
(5/x) + (1/x^2)
Evaluate the limit: lim (x -> 2) (x^2 - 4)/(x - 2).
0
2
8
4
What is the domain of the function f(x) = (1)/(x^2 - 4)?
All real numbers except x = 2 and x = -2.
Only x = 2 and x = -2 are excluded.
All real numbers except x = 0 and x = 1.
All real numbers including x = 2 and x = -2.
Identify the vertical asymptotes of the function f(x) = (x + 1)/(x^2 - 1).
x = -2
x = 2
x = 0
x = 1, x = -1
Simplify the expression (x^2 - 9)/(x^2 - 6x + 9).
(x + 3)/(x - 3)
(x + 3)/(x + 3)
(x^2 + 9)/(x^2 - 6x + 9)
(x - 3)/(x + 3)
Perform the operation: (x^2 + 2x)/(x^2 - 1) - (x - 1)/(x + 1).
(4x - 1)/((x - 1)(x + 1))
(x^2 - 2)/(x^2 + 1)
(2x + 3)/((x - 1)(x + 1))
(x + 1)/(x - 1)
Evaluate the limit: lim (x -> 0) (1/x).
The limit is infinity.
The limit is 0.
The limit does not exist.
The limit is 1.
What is the horizontal asymptote of the function f(x) = (3x^2 + 2)/(2x^2 + 5)?
y = 3/2
y = 5/2
y = 2/3
y = 0
Graph the function f(x) = (x - 1)/(x^2 + 1). What is the behavior as x approaches infinity?
1
0
undefined
-1
Identify the removable discontinuity in the function f(x) = (x^2 - 1)/(x - 1).
x = 0
x = -1
x = 1
x = 2
Perform the operation: (x + 2)/(x - 3) * (x - 3)/(x + 1).
(x + 2)/(x - 1)
(x - 2)/(x + 1)
(x + 2)/(x + 1)
(x + 3)/(x - 3)
