Graphing Rational Functions Answers
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1
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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.
2
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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 = 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.
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
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 = 0, and the horizontal asymptote is at y = 1.
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 = 1, and the horizontal asymptote is at y = 0.
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 = 0.
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 = 0, and the horizontal asymptote is at y = negative 1.
5
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
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 = 28
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
9
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.10
How does the range of compare with the range of the parent function ?
A
The range of both f(x) and g(x) is all real numbersB
The range of both f(x) and g(x) is all nonzero real numbersC
The range of f(x) is all real numbers, the range of g(x) is all real numbers except 6D
The range of f(x) is all nonzero real numbers, the range of g(x) is all real numbers except 6Did you find these answers helpful?
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