Transformations of Functions — Test Answers
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21
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Consider the function f(x) = x3 + 0.5x – 1. Marjan needs to graph f(x) and g(x) = –f(x) – 3. His graphs are shown below.
A
No, the reflection should be over the x-axis, not the y-axis.B
No, the reflection should be over the y-axis, not the x-axis.C
Yes, g(x) is a reflection of f(x) over the y-axis followed by a translation of 3 units down.D
Yes, g(x) is a reflection of f(x) over the x-axis followed by a translation of 3 units down.22
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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.
23
Which transformations to the graph of j(x) would result in the graph of j(4x) – 27?
A
horizontal stretch by a factor of 4, and a translation 27 units rightB
horizontal stretch by a factor of 4, and a translation 27 units downC
horizontal compression by a factor of , and a translation 27 units right
D
horizontal compression by a factor of , and a translation 27 units down24
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.
25
The graph models the projected populations, in thousands, of two towns after x years. Both towns experience a 1.9% annual growth rate.
A
g(x) = f
B
g(x) = f
C
g(x) = f(x) +
D
g (x) = five-thirds times f (x)
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