Graphing Rational Functions Answers
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1
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What is the domain of the function ?
A
all real numbersB
all real numbers except –1C
all real numbers except –4 and –2D
all real numbers except 2 and 42
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Which graph represents the function ?
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 0.
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 1.
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = negative 2, and the horizontal asymptote is at y = 4.
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
3
What are the vertical and horizontal asymptotes of ?
A
horizontal asymptote at y = 0, vertical asymptote at x = 1B
horizontal asymptote at y = 2, vertical asymptote at x = 1C
horizontal asymptote at y = 1, vertical asymptote at x = 0D
horizontal asymptote at y = 1, vertical asymptote at x = 24
What is the domain of ?
A
all real numbersB
all nonzero numbersC
all real numbers except 1D
all real numbers except 35
What is the horizontal asymptote of the function ?
A
y = 0B
y = 1C
y = 2D
y = 36
How does the graph of compare to the graph of the parent function ?
A
g(x) is shifted 5 units left and 2 units up from f(x).B
g(x) is shifted 5 units right and 2 units up from f(x).C
g(x) is shifted 5 units left and 2 units down from f(x).D
g(x) is shifted 5 units right and 2 units down from f(x).7
Which statement describes the behavior of the function ?
A
The graph approaches –3 as x approaches infinity.B
The graph approaches 0 as x approaches infinity.C
The graph approaches 3 as x approaches infinity.D
The graph approaches 4 as x approaches infinity.8
Which graph represents the function ?
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = negative 4.
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = negative 4.
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 4.
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
9
Which function has no horizontal asymptote?
A
f (x) = StartFraction 2 x minus 1 Over 3 x squared EndFraction
B
f (x) = StartFraction x minus 1 Over 3 x EndFraction
C
f (x) = StartFraction 2 x squared Over 3 x minus 1 EndFraction
D
f (x) = StartFraction 3 x squared Over x squared minus 1 EndFraction
10
What are the vertical and horizontal asymptotes for the function ?
A
horizontal asymptote: y = –2, y = 2vertical asymptote: x = 3B
horizontal asymptote: y = –4, y = 1vertical asymptote: x = 3C
horizontal asymptote: y = 3vertical asymptote: x = –4, x = 1D
horizontal asymptote: y = 3vertical asymptote: x = –2, x = 2Did you find these answers helpful?
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