Graph Transformtions

Question

given g(x)=3(cube root of -x)+6  describe the transformations in the appropriate order. Create a sketch of the new function and label 3 points.

 

I was unsure of how to put in a cube root symbol but the only thing underneath it in the equation is -x and the +6 is not under it.

I know the basic function this derives from is y=cube root of x but i am not quite sure how to preform the transformations when using 3 points.

 

The points I chose to use were (-1,1) (0,0) and (1,1) assuming if these are correct points to use (if not please explain why and which ones) then I believe that:

First, I would first do a reflection of the y-axis which would change the signs of the x values.

Next, I would do a vertical stretch multiplying the y values by 3

Lastly, I would do a vertical shift up 6 units.

 

However, I am not sure how to represent this with the coordinate points.

 

If my logic/steps are incorrect please inform me and explain the correct way to go about it.

 

Thank you!

Answer 1

The cube root of x is equivalent to x^1/3

 

g(x) = 3(-x)^1/3 + 6

 

Start with the graph of the "parent" function, y = x^1/3

 

Reflect in the y-axis to get the graph of y = (-x)^1/3

 

Vertically stretch the graph of y = (-x)^1/3 by a factor of three to get the     graph of y = 3(-x)^1/3

 

Vertically shift the graph of y = 3(-x)^1/3 six units upward to obtain the       graph of g(x) = 3(-x)^1/3 + 6.

 

Three points on the graph of the parent function are (-1,-1) (0,0) and (1,1).

 

Following the steps outlined above, these points are transformed as follows:

 

(-1,-1)→(1,-1)→(1,-3)→(1,3)

 

(0,0)→(0,0)→(0,0)→(0,6)

 

(1,1)→(-1,1)→(-1,3)→(-1,9)