#1
Which of the following is the graph of a rational function?
Circle
Parabola
Hyperbola
Line
#2
What is the vertical asymptote of the function f(x) = 1 / (x - 2)?
#3
What is the behavior of the rational function f(x) = 1 / x as x approaches infinity?
The function approaches 0 from the positive side.
The function approaches positive infinity.
The function approaches negative infinity.
The function oscillates.
#4
Which of the following is NOT a factor affecting the graph of a rational function?
Numerator degree
Denominator degree
Leading coefficient
Constant term
#5
What is the behavior of the rational function f(x) = (2x^3 - 5x^2 + 3x) / (x^2 - 4x + 3) as x approaches 3?
The function approaches a finite limit.
The function approaches positive infinity.
The function approaches negative infinity.
The function has a vertical asymptote at x = 3.
#6
What is the horizontal asymptote of the function f(x) = (3x^2 + 2) / (2x^2 - 1)?
#7
What does the behavior of the rational function f(x) = (x^2 - 4) / (x - 2) near x = 2 indicate?
There is a hole at x = 2
There is a vertical asymptote at x = 2
There is a horizontal asymptote at y = 2
There is a horizontal asymptote at y = 0
#8
What is the domain of the function f(x) = 3 / (x^2 - 4x + 4)?
All real numbers
All real numbers except x = 2
All real numbers except x = 4
All real numbers except x = 2 and x = 4
#9
What transformation does the function f(x) = (x + 3) / (x - 2) undergo compared to the function g(x) = 1 / x?
Vertical stretch
Horizontal compression
Vertical shift
Horizontal shift
#10
What is the slant asymptote of the function f(x) = (x^3 - 2x^2 + 5) / (x - 2)?
y = x + 1
y = x^2 - 4x + 9
y = x^2 + 4x - 1
y = x^2 + 2x + 3
#11
What is the slant asymptote of the function f(x) = (2x^2 + 3x - 1) / (x - 1)?
y = 2x + 3
y = 2x
y = 3x - 1
y = 2x - 1
#12
Which of the following rational functions has a slant asymptote?
f(x) = x / (x - 1)
f(x) = (x^2 + 3x + 2) / (x + 1)
f(x) = (x^3 + 2x + 1) / (x^2 + 1)
f(x) = (2x^2 + 3x - 1) / (x - 1)
#13
What is the behavior of the rational function f(x) = (x^2 - 3x + 2) / (x - 1) as x approaches infinity?
The function approaches a finite limit.
The function approaches positive infinity.
The function approaches negative infinity.
The function has a vertical asymptote at x = 1.
#14
What is the horizontal asymptote of the function f(x) = (2x^3 + x^2 - 1) / (3x^3 + 4x + 5)?
y = 2/3
y = 1/2
y = 3/4
y = 0
#15
What is the slant asymptote of the function f(x) = (2x^3 + 3x^2 - 1) / (x^2 + 2)?
y = 2x
y = 2x + 3
y = x^2 + 2
y = 2x^2 + 3x - 1