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Practice Problem #1

Graph the cube root function.

y equals negative the cube root of x plus 3 minus 1

What is the vertex of the function?

( , )

Complete your x-y table. Remember your vertex is in the middle. Choose two values
less than the x-value of the vertex and two values greater than the x-value of the vertex.

x y
-5  
-4  
-3 -1
-2  
-1  

Complete the top part of your x-y table. Remember if you have a decimal to round to the nearest hundredth. Be careful with the negative in front of the radical.

Substitute x = -5. What will you get?

Substitute x = -4. What will you get?

Substitute x = -2. What will you get?

Substitute x = -1. What will you get?

Plot the points on the coordinate plane.

A coordinate plane with the following points plotted: (negative 5, 0.26), (negative 4, 0), (negative 3, -1), (negative 2, negative 2), and (negative 1, negative 2,26).

Draw your graph to look like a cube root function. This graph was reflected over the x-axis because of the leading negative.

A graph of a cube root function with a vertex at (negative 3, negative 1) and points: (negative 5, 0.26), (negative 4, 0), (negative 2, negative 2), and (negative 1, negative 2.26). The graph decreases from left to right.

Practice Problem #2

Graph the cube root function.

y equals 2 the cube root of 3 x minus 6 plus 2

Use GeoGebra to do the graph and then sketch it on the coordinate plane.

A graph of a cube root function with a vertex at (2,2) and points: (4,5), (4, 5.6 ), (negative 1, negative 1), and (0, negative 1.6). The graph increases from left to right.

Practice Problem #3

Describe how the new graph (in red) was transformed from the parent graph (in gray).

y equals 2 the cube root of x plus 3

A graph of the parent graph of a cube root function in grey and a graph of a cube root function graphed in red with a vertex at (3, 0) increasing from left to right getting closer to the y-axis.

Practice Problem #4

Describe how the new graph (in red) was transformed from the parent graph (in gray).

y equals negative the cube root of 2 x minus 4 plus 3

A graph of the parent graph of a cube root function in grey and a graph of a cube root function graphed in red with a vertex at (2,3) decreasing from left to right getting further away from the x-axis.