write a rule for g described by the transformation of the graph of f

Question

write a rule for g described by the transformation of the graph of d then identify the vertex. f(x)=x^2 vertical shrink by factor of 1/2 units, 4 units to the right and 5 units down 

Answer 1

f(x) = x is the base function.

 

To shrink it vertically by 1/2, make 1/3 the coefficient of the variable x.

 

To shift it 4 units to the right, subtract 4 from within the squared variable.

 

To shift 5 units down, subtract 5 from the entire function.

 

That leaves us with the following function:

 

    f(x) = (1/2)(x - 4)² - 5