#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
If the degree of the numerator is greater than the degree of the denominator in a rational function, what can be concluded about the end behavior?
It approaches positive infinity on both ends
It approaches negative infinity on both ends
It has a horizontal asymptote
The end behavior cannot be determined
#8
What is the oblique asymptote of the rational function f(x) = (4x^2 + 2)/(x - 1)?
y = 4x
y = 4x + 2
y = 4
There is no oblique asymptote
#9
What is the limit of the rational function (2x^2 - 5x + 3)/(x^2 + 2x - 3) as x approaches 1?
#10
For the rational function f(x) = (x^2 + 4)/(x - 2), what is the vertical asymptote?
x = 2
x = 4
x = -2
There is no vertical asymptote
#11
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
#12
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
#13
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
#14
For the rational function g(x) = (x^2 - 4)/(x - 2), what is the hole's x-coordinate?
#15
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
#16
What is the degree of the numerator in the rational function h(x) = (2x^3 + 4x^2 + 1)/(x^2 - 1)?
#17
Which statement is true regarding the graph of a rational function with a hole?
The hole indicates a vertical asymptote
The hole is a point of discontinuity
The hole is always at the origin
The hole implies a slant asymptote
#18
For the rational function g(x) = (2x^2 - 5)/(x + 1), what is the horizontal asymptote?
y = 2
y = -5
y = 0
There is no horizontal asymptote
#19
What is the behavior of a rational function as it approaches a vertical asymptote?
It crosses the asymptote
It has a hole
It approaches infinity or negative infinity
It oscillates
#20
For the rational function h(x) = (x^2 - 1)/(x + 1), what is the value of the hole?
#21
If a rational function has a vertical asymptote at x = -4 and a hole at x = 2, what can be said about the function?
The function is undefined at x = -4
The function has a slant asymptote
The function has a removable discontinuity
The function has a horizontal asymptote
#22
What is the degree of the denominator in the rational function g(x) = (3x^3 + 2)/(2x^2 - x + 1)?
#23
Which statement is true about the behavior of a rational function near a hole?
The function has a vertical asymptote at the hole
The function is undefined at the hole
The function approaches a finite value at the hole
The hole indicates a slant asymptote
#24
If a rational function has a horizontal asymptote at y = -3, what can be inferred?
The function approaches -3 as x approaches infinity
The function has a hole at y = -3
The function has a vertical asymptote at y = -3
The function is undefined at y = -3
#25
What is the end behavior of the rational function g(x) = (4x^3 - 2)/(2x^2 + 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