graph g(x) = 3(x-1/2)^3-1

Question

graph this using transformations.

Answer 1

The equation is .

Make a table for the above equation.

Draw the graph of the equation .

1.Draw a co-ordinate plane.

2.Plot the points.

3.Draw a smooth curve through this points.

Answer 2

The function is g ( x ) = 3(x - 1/2)³ - 1.

The heighest power of x in g ( x ) = 3(x - 1/2)³ - 1 is 3, so the parent function is cubic function.

The equation of parent function is f ( x ) = x³ .

The transformation function is g ( x ) = 3(x - 1/2)³ - 1 and the parent function is f ( x ) = x³ .

So, the functions f and g have the following relationship.

g ( x ) = 3f ( x - 1/2 ) - 1.

To transform the graph of f ( x ) = x³ into the graph of  g(x) follow the steps :

Step 1 :

The graph of g (x) is a right shift of 1/2 units(each y - value is subtracted by 1/2 of the graph of f (x)).

Then,  the function g (x) = (x - 1/2)² .

Step 2 :

The graph of g (x) is the vertical stretch (each y - value is multiplied by 3) of the graph of f (x).

Then,  the function g (x) = 3(x - 1/2)² .

Step 3 :

The graph of g (x) is the vertical shift(down ward) of one unit of the graph of f ( x ).

Then, the function is g (x) = 3(x - 1/2)² -1.

The functions f and g are related as follows :