Algebra 1 Graphing Cube Root Functions WS

Name: ____________________ Block: ________

Directions: Graph the following cube root functions. Label key points, list transformations, and describe the domain and range. 2) g ( x) 

f ( x)  2 3 x

1)

x

y

x

y

x

y

3

x 3

x

y

3) y 

x

y

3

x 1  4

x

y

Domain: ___________

Domain: ___________

Domain: ___________

Range: ___________

Range: ___________

Range: ___________

Transformations:

Transformations:

Transformations:

4) Consider the two functions from above for #1 and #2, f ( x)  2 3 x and g ( x)  of the following is true or false.

3

x  3 . Decide whether each

_____ The y-intercept of the graph f(x) is greater than the y-intercept of the graph g(x). The y-intercept of the graph f(x) is _____. The y-intercept of the graph g(x) is ______. _____The average rate of change of g(x) is greater than the average rate of change of f(x) over the interval x = 0 to x = 8. Show ALL of your work below.

6) y 

5) y   3 x  2

x

y

x

y

x

y

13 x 2 2

x

y

7) y  2 3 x  3  6

x

y

x

y

Domain: ___________

Domain: ___________

Domain: ___________

Range: ___________

Range: ___________

Range: ___________

Transformations:

Transformations:

Transformations:

8) Write an equation for a cube root function with transformations of: reflection over the x-axis, vertical shift down 1, and horizontal shift right 3.