Rational Functions and Their Properties Quiz
Challenge yourself with questions on rational functions, covering domains, asymptotes, behavior, and more. Test your understanding now!
#1
Which of the following is a rational function?
y = sqrt(x)
y = (3x + 2)/(x - 1)
y = e^x
y = |x|
#2
What is the domain of the rational function f(x) = (2x - 1)/(x + 3)?
All real numbers except x = 3
All real numbers except x = -3
All real numbers
Only x = 3
#3
Which of the following functions is not a rational function?
y = 5x + 1
y = (x^2 + 3)/(2x + 1)
y = sin(x)
y = 1/(x + 2)
#4
What is the slant asymptote of the rational function f(x) = (3x^2 + 2)/(x + 1)?
y = 3x
y = 3x + 2
y = 3
There is no slant asymptote
#5
If a rational function has a degree of 2 in the numerator and 3 in the denominator, what can be said about its end behavior?
It approaches positive infinity on both ends
It approaches negative infinity on both ends
It has a slant asymptote
The end behavior cannot be determined
#6
What is the domain of the rational function f(x) = (x^2 - 9)/(x - 3)?
All real numbers except x = 3
All real numbers except x = -3
All real numbers
Only x = 3
#7
Which statement is true about the vertical asymptotes of a rational function?
They occur where the numerator is zero
They occur where the denominator is zero
They occur at x = 0
They occur at x = 1
#8
If a rational function has a horizontal asymptote at y = 2, what can be inferred?
The function has a hole at y = 2
The function approaches 2 as x approaches infinity
The function approaches 2 as x approaches negative infinity
The function has a vertical asymptote at y = 2
#9
What is the end behavior of the rational function f(x) = (3x^2 + 2)/(2x^2 - x + 1)?
Approaches positive infinity as x approaches infinity
Approaches negative infinity as x approaches negative infinity
Approaches zero as x approaches infinity
Approaches a constant value as x approaches infinity
#10
For the rational function g(x) = (x^2 - 4)/(x - 2), what is the hole's x-coordinate?
#11
If a rational function has a vertical asymptote at x = -5 and a hole at x = 3, what can be said about the function?
The function has a slant asymptote
The function is undefined at x = -5
The function has a removable discontinuity
The function has a horizontal asymptote
#12
What is the degree of the numerator in the rational function h(x) = (2x^3 + 4x^2 + 1)/(x^2 - 1)?
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