Which of the following sequence of shifts would you perform in order to obtain the graph of f(x) = (x - 4)² + 1

from the graph of g(x) = x²

A.) Shift the graph of g up 1 unit and then left 4 units

B.) Shift the graph of g down 1 unit and then right 4 units

C.) Shift the graph of g up 1 unit and then right 4 units

D.) Shift the graph of g down 4 units and then right 1 unit

E.) none of these

from the graph of g(x) = x²

A.) Shift the graph of g up 1 unit and then left 4 units

B.) Shift the graph of g down 1 unit and then right 4 units

C.) Shift the graph of g up 1 unit and then right 4 units

D.) Shift the graph of g down 4 units and then right 1 unit

E.) none of these

When you subtract 4 from the x-value, it shifts the graph right 4 units on the x-axis {that is shown in (x - 4)}

When you add 1 to the y-value, it shifts the graph up 1 on the y-axis {that is shown by adding 1 to what f(x) equals}

The right and left shifts are easily misunderstood and confused.

Remember:

- when you subtract from the x-value, it shifts the graph to the right, and

when you add to the x-value it shifts the graph to the left

{opposite of what most people think it should be}

Also,

- when you add to the y-value, it shifts the graph up, and

when you subtract from the y-value, it shifts the graph down

**C.) Shift the graph of g up 1 unit and then right 4 units**

*- Algebra House*