AnswersAlgebra 2 with ProbabilityTransformations of Functions

Transformations of Functions — Quiz Answers

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1
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How is the graph of the parent function y is equal to x squared transformed to produce the graph of y is equal to 3 times open paren x plus 1 close paren squared ?

A
It is translated 1 unit left and compressed vertically by a factor of 3 .
B
It is translated 1 unit right and compressed vertically by a factor of 3 .
C
It is translated 1 unit left and stretched vertically by a factor of 3 .
D
It is translated 1 unit right and stretched vertically by a factor of 3 .
2
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Which graph is an example of a cubic function?

A
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. A straight line with a positive extending infinitely in both positive x and y directions.
B
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. There is a curve that approaches x equals negative 2 in quadrant 3, increases to a point of inflection at (0, 1), and then increases again and approaches x equals 2.
C
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The V-shaped graph opening downwards has a vertex at (0 comma 1) and the graph cuts the x axis at (negative 0 point 5 comma 0) and (0 point 5 comma 0).
D
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The parabola opens upwards and has a vertex at (negative 1 comma 0) and cuts the y axis at (0 comma 1).
3

Which of the following is the graph of y is equal to negative open paren x minus 2 close paren cubed minus 5 ?

A
Image with description On a coordinate plane, the scale on the x axis range from negative 5 to 5 in increments of 1, and the scale on the y axis range from negative 10 to 0 in increments of 1. The curve lies in the 3rd quadrant and passes through points (negative 3 point 5 comma negative 3) and (negative 1 comma negative 6). It has the point of inflection at (negative 2 comma negative 5).
B
Image with description On a coordinate plane, the scale on the x axis ranges from negative 5 to 5 in increments of 1, and the scale on the y axis ranges from negative 10 to 0 in increments of 1. The curve lies in the 4th quadrant and passes through points (1 comma negative 3) and (4 comma negative 9). It has the point of inflection at (2 comma negative 5).
C
Image with description On a coordinate plane, the scale on the x axis ranges from negative 5 to 5 in increments of 1, and the scale on the y axis ranges from negative 10 to 0 in increments of 1. The curve lies in the 4th quadrant and passes through points (3 point 5 comma negative 2) and (1 comma negative 7). It has the point of inflection at (2 comma negative 5).
D
Image with description On a coordinate plane, the scale on the x axis ranges from negative 5 to 5 in increments of 1, and the scale on the y axis ranges from negative 10 to 0 in increments of 1. The curve lies in the 3rd quadrant and passes through points (negative 1 comma negative 3) and (negative 4 comma negative 10). It has the point of inflection at (negative 2 comma negative 5).
4

For which graph is the parent function y is equal to x squared ?

A
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. A straight line with a positive slope extending infinitely is drawn. It passes through (1 point 5 comma 0) and (0 comma 3).
B
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. There is a cubic curve that passes through points (negative 1 comma negative 4), (0 comma 1), and (3 comma 5). The curve has a point of inflection at (1 comma 2).
C
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. There is a parabola that opens upwards and has a vertex at (negative 1 comma negative 2) and cuts the x axis at (negative 3 comma 0) and (1 comma 0).
D
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The V-shaped graph opening upwards has a vertex at (1 comma negative 2) and the graph cuts the x axis at (negative 1 comma 0) and (3 comma 0).
5

To which family does the function y is equal to open paren x plus 2 close paren raised to the 1 half power plus 3 belong?

A
exponential
B
square root
C
quadratic
D
reciprocal
6

To which family does the function y is equal to 2 to the x th power plus 5 belong?

A
square root
B
exponential
C
logarithmic
D
quadratic
7

The value of a graphed function doubles for each increase of 1 in the value of x Which of the following could be the parent function of the graphed function?

A
y is equal to square root of x
B
y is equal to 2 to the x th power
C
y is equal to x squared
D
y is equal to absolute value of 2 x
8

How is the graph of the parent quadratic function transformed to produce the graph of y is equal to negative open paren 2 x plus 6 close paren squared plus 3 ?

A
The graph is reflected over the x -axis, stretched horizontally by a factor of 2 , shifted left 6 units, and translated up 3 units.
B
The graph is stretched horizontally by a factor of 2 , reflected over the x -axis, shifted left 3 units, and translated up 3 units.
C
The graph is compressed horizontally by a factor of 2 , shifted left 3 units, reflected over the x -axis, and translated up 3 units.
D
The graph is reflected over the x -axis, compressed horizontally by a factor of 2 , shifted left 6 units, and translated up 3 units.
9

Which graph is an example of a function whose parent function is y is equal to square root of x ?

A
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The parabola opens upwards, has a vertex at (0 comma 1).
B
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. 2 curves are drawn. Both curves have an asymptote at x equals negative 1. One curve decreases from quadrant 2 into quadrant 1 and approaches y equals 1. It crosses the y-axis at (0 comma 2). The other curve approaches y equals 1 in quadrant 1 and then curves down and approaches y equals negative 1 in quadrant 3. It crosses the x axis at (negative 2, 0).
C
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The curve starts in quadrant 3 and then increases into quadrant 1. It crosses y axis at (0 comma negative 2) and crosses the x axis at (1 point 5 comma 0).
D
Image with description On a coordinate plane, the x and y axes list from negative 5 to 5 in increments of 1. The curve starts at (negative 4 comma negative 1), passes through (negative 3 comma 0) and then curves up and increases to the right into quadrant 1.
10

The graph of a quadratic function, y is equal to x squared , is reflected over the x -axis. Which of the following is the equation of the transformed graph?

A
y is equal to negative x squared
B
y is equal to negative square root of x
C
y is equal to square root of negative x
D
y is equal to negative x squared

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