AnswersEAP-Algebra Functions and Data Analysis A CRTransformations of Functions

Transformations of Functions Answers

0 verified answers2 views
1
Free Preview

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a cubic root function approaches the negative y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then increases and approaches x = 4.
Option A
B
On a coordinate plane, a cubic root function approaches x = negative 5 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then approaches the y-axis in quadrant 3.
Option B
C
On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4.
Option C
D
On a coordinate plane, a cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then decreases and approaches the negative y-axis in quadrant 3.
Option D
2
Free Preview

The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

Question illustration
A
y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2
Option A
B
y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2
Option B
C
y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3
Option C
D
y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3
Option D
3

Which equation describes how the parent function, , is vertically stretched by a factor of 4?

Question illustration
A
y = x cubed + 4
Option A
B
y = (x + 4) cubed
Option B
C
y = 4 x cubed
Option C
D
y = x Superscript 4
Option D
4

To which family does the function belong?

Question illustration
A
quadratic
B
square root
C
exponential
D
reciprocal
5

Which results only in a horizontal compression of by a factor of 6?

Question illustration
A
y = StartFraction 1 Over 6 x EndFraction
Option A
B
y = negative StartFraction 1 Over 6 x EndFraction
Option B
C
y = StartFraction 6 Over x EndFraction
Option C
D
y = negative StartFraction 6 Over x EndFraction
Option D
6

Which equation represents the transformed function below?_____ = parent function; - - - - - = transformed function

Question illustration
A
y = StartRoot x + 2 EndRoot
Option A
B
y = StartRoot x EndRoot + 2
Option B
C
y = StartRoot x EndRoot minus 2
Option C
D
y = StartRoot x minus 2 EndRoot
Option D
7

Which graph is an example of a function whose parent function is ?

Question illustration
A
On a coordinate plane, a curve starts at (negative 1, negative 1) and then curves up and to the right into quadrant 1.
Option A
B
On a coordinate plane, a parabola has a vertex at (0, 1).
Option B
C
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 1. One curved decreases from quadrant 2 into quadrant 1 and approaches y = 1. It crosses the y-axis at (0, 2). The other curve approaches y = 1 in quadrant 1 and then curves down and approaches y = negative 1 in quadrant 3. It crosses the x-axis at (negative 2, 0).
Option C
D
On a coordinate plane, a curve starts in quadrant 3 and then increases into quadrant 1. It crosses the y-axis at (0, negative 2) and crosses the x-axis at (1.5, 0).
Option D
8

To which family does the function belong?

Question illustration
A
quadratic
B
square root
C
exponential
D
logarithmic
9

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve opens down and to the right and approaches y = 0 in quadrant 4. It increases into quadrant 1 and goes through (1, 3) and (4, 6).
Option A
B
On a coordinate plane, a curve opens down and to the right and approaches y = negative 3 in quadrant 3. It increases into quadrant 1 and goes through (negative 2, 0) and (1, 3).
Option B
C
On a coordinate plane, a curve approaches x = negative 3 in quadrant 4 and increases into quadrant 1. It goes through (4, 0) and (7, 3).
Option C
D
On a coordinate plane, a curve approaches y = 0 in quadrant 4 and then increases into quadrant 1. It goes through (4, 0) and (6, 1).
Option D
10

The velocity of a particle can be modeled by the function . Which graph accurately shows the velocity of the particle at any time, t?

Question illustration
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.
Option A
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.
Option B
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.
Option C
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.
Option D
11

How is the graph of the parent function transformed to produce the graph of ?

Question illustration
A
It is translated 1 unit right and compressed vertically by a factor of 3.
B
It is translated 1 unit left and compressed vertically by a factor of 3.
C
It is translated 1 unit right and stretched vertically by a factor of 3.
D
It is translated 1 unit left and stretched vertically by a factor of 3.
12

A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The function represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function transformed to create the graph of the function ?

Question illustration
A
It is a vertical stretch with a factor of 100 and a translation 5 units right.
B
It is a vertical stretch with a factor of 95.
C
It is a vertical stretch with a factor of 100 and a translation 5 units down.
D
It is a vertical stretch with a factor of 500.
13

For which graph is the parent function ?

Question illustration
A
On a coordinate plane, a parabola opens up and has a vertex at (negative 1, negative 2).
Option A
B
On a coordinate plane, a straight line has a positive slope.
Option B
C
On a coordinate plane, a cubic root function is shown.
Option C
D
On a coordinate plane, an absolute value function is shown.
Option D
14

How is the graph of the parent function transformed to create the graph of ?

Question illustration
A
It is horizontally stretched by a factor of 3 and reflected over the y-axis.
B
It is translated 3 units down and reflected over the x-axis.
C
It is horizontally compressed by a factor of 3 and reflected over the x-axis.
D
It is translated 3 units down and reflected over the y-axis.
15

The graph of the function is shown.Which graph represents the function ?

Question illustration
A
On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (1, 2) and (2, 1). The other curve opens down and to the left in quadrant 3 and goes through (negative 2, negative 1) and (negative 1, negative 2).
Option A
B
On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (2, 2.5). The other curve opens down and to the left in quadrants 2 and 3 and goes through (negative 0.5, 0) and (negative 2, 1.5).
Option B
C
On a coordinate plane, 2 curves have an asymptote at y = negative 2. On curve opens up and to the right in quadrants 1 and 2 and goes through (negative 1, 1) and (0, 0.5). Another curve opens down and to the right in quadrant 3 and goes through (negative 3, negative 1) and (negative 2.5, negative 2).
Option C
D
On a coordinate plane, 2 curves have an asymptote at y = 0. One curve opens up and to the right in quadrant 1 and goes through (0.5, 1) and (1, 0.5). The other curve opens down and to the left in quadrant 3 and goes through (negative 1, negative 0.5) and (negative 0.5, negative 0.5).
Option D
16

How is the graph of the parent function of transformed to produce the graph ?

Question illustration
A
It is horizontally stretched by a factor of .
Option A
B
It is vertically stretched by a factor of .
Option B
C
It is translated left by unit.
Option C
D
It is translated right by unit.
Option D
17

The graph below belongs to which function family?

Question illustration
A
linear
B
quadratic
C
cubic
D
absolute value
18

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 ?

Question illustration
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.

Did you find these answers helpful?

More from this Course

Quiz
20 verified answers

Transformations of Functions

Quiz
14 verified answers

Transformations of Functions

Quiz
12 verified answers

Unit Test