Transformations of Functions Answers
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1
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For which graph is the parent function ?
A
On a coordinate plane, a parabola opens up and has a vertex at (negative 1, negative 2).
B
On a coordinate plane, a straight line has a positive slope.
C
On a coordinate plane, a cubic root function is shown.
D
On a coordinate plane, an absolute value function is shown.
2
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To which family does the function belong?
A
quadraticB
square rootC
exponentialD
logarithmic3
How is the graph of the parent function of transformed to produce the graph ?
A
It is horizontally stretched by a factor of .
B
It is vertically stretched by a factor of .
C
It is translated left by unit.
D
It is translated right by unit.
4
The velocity of a particle can be modeled by the function . Which graph accurately shows the velocity of the particle at any time, t?
A
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2.5, negative 2), and then increases into quadrant 2 and approaches x = negative 1.
B
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = 1 in quadrant 1, has a point of inflection at (2.5, negative 2), and then increases into quadrant 1 and approaches x = 4.
C
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function approaches x = 1 in quadrant 1, has a point of inflection at (2.5, 2), and then decreases into quadrant 4 and approaches x = 5.
D
On a coordinate plane, the x-axis is labeled time and the y-axis is labeled velocity. A cubic root function starts in quadrant 4 and increases into quadrant 1. It has a point of inflection at (8, 2) and then it continue to increase in quadrant 1.
5
The function models the cost per student of a field trip when x students go on the trip. How is the parent function transformed to create the function ?
A
It is vertically stretched by a factor of 200.B
It is vertically stretched by a factor of 200 and shifted 10 units left.C
It is vertically stretched by a factor of 200 and shifted 10 units up.D
It is vertically stretched by a factor of 200 and shifted 10 units right.6
Which results only in a horizontal compression of by a factor of 6?
A
y = StartFraction 1 Over 6 x EndFraction
B
y = negative StartFraction 1 Over 6 x EndFraction
C
y = StartFraction 6 Over x EndFraction
D
y = negative StartFraction 6 Over x EndFraction
7
The graph of is shown.Which is the graph of ?
A
On a coordinate plane, a cubic root function is shown. It approaches x = negative 3 in quadrant 3, has an inflection point at (negative 1, negative 2), and then approaches y = 2 in quadrant 1. It crosses the y-axis at (0, negative 2).
B
On a coordinate plane, a cubic root function is shown. It approaches x = negative 1 in quadrant 3, has an inflection point at (2, 1), and then increases and approaches y = 5.
C
On a coordinate plane, a cubic root function is shown. It approaches the y-axis in quadrant 4, increases, has a point of inflection at (2, 1), and then increases and approaches x = 4.
D
On a coordinate plane, a cubic root function is shown. It approaches the y-axis in quadrant 2, decreases, has a point of inflection at (negative 2, 1), and then decreases and approaches x = negative 4.
8
To which family does the function belong?
A
quadraticB
square rootC
exponentialD
reciprocal9
The graph below belongs to which function family?
A
linearB
quadraticC
cubicD
absolute value10
The graph of is transformed as shown in the graph below. Which equation represents the transformed function?
A
y = StartAbsoluteValue one-fourth x EndAbsoluteValue
B
y = StartAbsoluteValue 2 x EndAbsoluteValue
C
y = StartAbsoluteValue 4 x EndAbsoluteValue
D
y = StartAbsoluteValue one-half x EndAbsoluteValue
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