Transforming Polynomial Functions

Question

Identify the function that vertically stretches f(x)=-4x^3+1 by a factor of 2 and shifts 7 units left. 

 

h(x)=-8(x-7)^3+1

h(x)=-8(x+7)^3+1

h(x)=-8(x-7)^3+2

h(x)=-8(x+7)^3+2

Answer 1

To vertically stretch the function by a factor of 2, multiply by 2  to get                     y = -8x³+2.  To then shift that graph 7 units leftward, replace x by x+7 to obtain                         

                    y = -8(x+7)³+2

Answer 2

Vertical stretch of 2 means to multiply the leading coefficient by 2.   When you shift a function c units to the left, the piece of the function is (x + c). 

 

There is no vertical shift.

 

 

Your answer is    h(x) = -8(x + 7)³ + 1