WorksheetsGraphing Cubic and Cube Root Transformations
Total questions: 20
Worksheet time: 20mins
If f(x) = ∛(x) is reflected over the x-axis, vertically shrunk by a factor of 1/4, and shifted left 9, which equation is correct?
1/4 ∛(x + 9)
1/4 ∛(x - 9)
- 1/4 ∛(x + 9)
- 1/4 ∛(x - 9)
Which of the facts is not true about the graph shown?
The range is all real numbers.
The function has been shifted 6 units right.
The function has been shifted up 1 unit
The function has been vertically stretched by a factor of 2.
What transformations have occurred to get from the parent function f(x) to the transformed function g(x)?
reflection over the x-axis,vertical shrink by a factor of -5
reflection over the x-axis,vertical shrink by a factor of 1/5
reflection over the x-axis,vertical stretch by a factor of 5
reflection over the y-axis,vertical stretch by a factor of 5
The graph of y=x3 is graphed in blue. Which of the following equations could be equation of the function graphed in red?
y=201(x−2)3+1
y=201(x+2)3+1
y=20(x−2)3+1
y=20(x+2)3+1
Which of the following is the graph of y = (x – 1)3 – 7?
What kind of fruits are best for a healthy diet?
Apples
Bananas
Oranges
Berries
If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?
1/4 ∛(x + 9)
1/4 ∛(x - 9)
- 1/4 ∛(x + 9)
- 1/4 ∛(x - 9)
The range is y ≥ 1
It has been reflected over the y-axis
The function has been shifted up 1 unit
The function has been shifted up 2 units
Shifted to the left 6
What transformations has the function undergone?
reflect over y, vertical compress by 2, right 5, up 1
reflect over x, horizontal compression by 2, left 5, up 1
reflect over x, vertical stretch by 2, right 5, up 1
reflect over y, horizontal stretch by -2, right 5, up 1
Identify the function that corresponds with the graph.
f(x)=3x+2−5
f(x)=3x−5+2
f(x) = 3x+5+2
The graph of a function is shown. What are the domain and range of this function?
Domain: (-∞, ∞)
Range: (-∞, 2]
Domain: [2, ∞)
Range: (-∞, ∞)
Domain: (-∞, ∞)
Range: (-∞, ∞)
Domain: (-∞, 2]
Range: [2, ∞)
If f(x) = x3 is changed to f(x) = - (x + 3)3 + 2, how is the graph transformed?
3 units right, 2 units up, reflected across the y-axis
3 units right, 2 units up, reflected across the x-axis
3 units left, 2 units up, reflected across the y-axis
3 units left, 2 units up, reflected across the x-axis
What is the equation of this function?
f(x) = (x + 2)3
f(x) = (x - 2)3
f(x) = ∛(x + 2)
f(x) = ∛(x - 2)
If a cubic function is shifted left what happens to the domain?
(−∞,∞)
−2<x<∞
(−2,0]
All Cube Root Functions are different.
Undefined
What is the factored form for the following cubic function?
x(x - 3)(x - 4)
x(x + 3)(x + 4)
x(x - 3)(x + 4)
(x + 3)(x - 3)(x - 4)
What transformations have occurred to get the graph of g(x) from the graph of f(x)?
vertical shrink by a factor of 1/4,translation down 2 units
vertical shrink by a factor of 1/4,translation right 2 units
vertical stretch by a factor of 1/4,translation down 2 units
vertical stretch by a factor of 1/4,translation right 2 units
What transformations have occurred to get the graph of g(x) from the graph of f(x)?
reflection over the x-axis,vertical compress by a factor of 5
reflection over the y-axis,vertical compress by a factor of 5
reflection over the x-axis,vertical stretch by a factor of 5
reflection over the y-axis,vertical stretch by a factor of 5
Identify the Transformations.
Vertical stretch by 2 and down 4
Horizontal compression by ½ and down 4
Vertical stretch by 2 and up 4
Horizontal compression by ½ and right 4
