Transforming Cubic Function

Which transformation is applied to the function y = x³ to obtain the graph shown?

• Shift left 1 unit and down 5 units

• Shift right 1 unit and up 5 units

• Shift left 3 units and down 2 units

• Shift right 2 units and down 3 units

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 for the red function?

• g(x)=x³+1

• g(x)=x³-1

• g(x)=(x-1)³

• g(x)=(x+1)³

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

• Stretch

• Compress

• x-axis

• y-axis

• Right

• Left

• Up

• Down

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

Write the equation for a cubic function that has been vertically compressed by a factor of 3, vertically shifted 5 units down, and horizontally shifted 7 units left.

Mathematical Equivalence

OFF

The graph shows the function f(x)=x³ in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x) = -x³

• g(x) = x³ - 1

• g(x) = (x + 1)³

• g(x) = (x - 1)³

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