#1
Which of the following is a rational function?
y = (3x + 2)/(x - 1)
ExplanationRatio of two polynomials
#2
What is the domain of the rational function f(x) = (2x - 1)/(x + 3)?
All real numbers except x = -3
ExplanationDenominator cannot be zero
#3
Which of the following functions is not a rational function?
y = sin(x)
ExplanationTrigonometric functions are not ratios of polynomials
#4
What is the slant asymptote of the rational function f(x) = (3x^2 + 2)/(x + 1)?
y = 3x
ExplanationOccurs when degree of numerator > degree of denominator by 1
#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
ExplanationLeading term comparison
#6
What is the domain of the rational function f(x) = (x^2 - 9)/(x - 3)?
All real numbers except x = -3
ExplanationDenominator cannot be zero
#7
Which statement is true about the vertical asymptotes of a rational function?
They occur where the denominator is zero
ExplanationDenominator determines vertical asymptotes
#8
If a rational function has a horizontal asymptote at y = 2, what can be inferred?
The function approaches 2 as x approaches infinity
ExplanationHorizontal asymptote defines limit behavior
#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
ExplanationLeading term comparison
#10
For the rational function g(x) = (x^2 - 4)/(x - 2), what is the hole's x-coordinate?
2
ExplanationFactor out common terms in numerator and denominator
#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 removable discontinuity
ExplanationRemovable discontinuity when both occur
#12
What is the degree of the numerator in the rational function h(x) = (2x^3 + 4x^2 + 1)/(x^2 - 1)?
3
ExplanationDegree of highest power term in numerator