Write the equation for the final transformed graph

Question

Let f(x)= x². Write the equation for the final transformed graph if the following transformations are
applied to f: stretch vertically by a factor of 2; shift downward by 5 units; shift right by 4 units.

 

 

Start with how we would write the new function, for example 5f(x − 1) + 9, and then expand the answer.

Answer 1

y = f(x) = x²

 

Stretching vertically by a factor of 2 gives y = 2x² = 2f(x).

 

If we then shift downward by 5 units, an equation of the resulting graph is y = 2x² - 5  (or y = 2f(x) - 5).

 

Finally, shifting rightward by 4 units, our equation becomes y = 2(x-4)² -5.

 

So, y = 2f(x-4) - 5.