AIgo NotesQuiz for:
How to Graph Cubic Functions Using Transformations
Question 17
In the function y = (x - 3)^3 + 2, what is the vertical shift from the parent function y = x^3?
A.2 units up
B.2 units down
C.3 units up
D.3 units down
Question 1
What is the parent function discussed in the video for graphing cubic functions using transformations?
A.y = x
B.y = x^3
C.y = |x|
D.y = x^2
Question 2
What happens to the graph if a negative sign is placed in front of the x^3 term?
A.The graph flips over the x-axis.
B.The graph flips over the y-axis.
C.The graph becomes a parabola.
D.The graph remains the same.
Question 3
How does the graph change when an absolute value symbol is placed in front of the x^3 term?
A.The graph reflects over the x-axis on the left side.
B.The graph reflects over the y-axis.
C.The graph becomes a parabola.
D.The graph remains the same.
Question 4
In the function y = x^3 + 2, how many units is the graph shifted up from the parent function y = x^3?
A.1 unit
B.2 units
C.3 units
D.4 units
Question 5
What is the horizontal shift for the function y = x^3 - 3?
A.No shift
B.Shifted left 3 units
C.Shifted right 3 units
D.Shifted up 3 units
Question 6
In the function y = (x - 2)^3, how many units is the graph shifted to the right?
A.1 unit
B.2 units
C.3 units
D.4 units
Question 7
For the function y = (x + 4)^3, how many units is the graph shifted to the left?
A.1 unit
B.2 units
C.3 units
D.4 units
Question 8
What is the center of the graph for the function y = (x - 3)^3?
A.(3, 0)
B.(0, 3)
C.(3, 3)
D.(3, -3)
Question 9
In the function y = |x - 3|^2 + 2, what is the vertical shift from the parent function y = |x|^2?
A.2 units up
B.2 units down
C.3 units up
D.3 units down
Question 10
What is the general form of a cubic function in standard form?
A.y = ax^2 + bx + c
B.y = ax^3 + bx^2 + cx + d
C.y = ax^3 + k
D.y = ax^3 + bx^2 + k
Question 11
How does a positive value of 'a' affect the graph of a cubic function?
A.It makes the graph decrease.
B.It makes the graph increase.
C.It makes the graph reflect over the y-axis.
D.It makes the graph reflect over the x-axis.
Question 12
In the function y = (x - 3)^3 + 2, what are the coordinates of the center of the graph?
A.(3, 0)
B.(3, 2)
C.(0, 3)
D.(3, -3)
Question 13
What is the purpose of creating a data table when graphing cubic functions?
A.To calculate the area under the curve.
B.To find the derivative of the function.
C.To plot points and sketch the graph accurately.
D.To determine the roots of the function.
Question 14
For the function y = (x + 1)^3 - 4, what is the horizontal shift from the parent function y = x^3?
A.No shift
B.Shifted left 1 unit
C.Shifted right 1 unit
D.Shifted up 1 unit
Question 15
What is the vertical shift for the function y = (x + 1)^3 - 4?
A.4 units up
B.4 units down
C.5 units up
D.5 units down
Question 16
How does a negative value of 'a' affect the graph of a cubic function?
A.It makes the graph increase.
B.It makes the graph decrease.
C.It makes the graph reflect over the y-axis.
D.It makes the graph reflect over the x-axis.
Question 17
In the function y = (x - 3)^3 + 2, what is the vertical shift from the parent function y = x^3?
A.2 units up
B.2 units down
C.3 units up
D.3 units down
Question 1
What is the parent function discussed in the video for graphing cubic functions using transformations?
A.y = x
B.y = x^3
C.y = |x|
D.y = x^2