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GeoGebra

Square Root and Cube Root Functions

Author:Tara Riba, wyattmg1

Transformations of Square Root and Cube Root Functions

In previous units we have studied transformations of linear, absolute value, and quadratic functions. Here we will study transformations on the square root and cube root functions.
Drag the sliders to change the graph of cube root and square root functions. Observe how changing each slider changes the function.

Square root functions of the form:

What do you think will happen when we adjust the value of a, h, and k?

Cube root functions of the form:

What do you think will happen when we adjust the value of a, h, and k?

Check your understanding

Which functions below show a graph with a vertical stretch by a factor of 3?

Select all that apply
  • A
  • B
  • C
  • D
  • E
Check my answer (3)

Which functions below show a translation 2 units up?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Which functions below show a translation 2 units right?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Enrichment

Write an equation for a vertical stretch by a factor of 2 followed by a translation 2 units left of the square root parent functions:

Enrichment

Write an equation for a vertical stretch by a factor of 2 followed by a translation 2 units left and 3 units down of the cube root parent functions:

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