Question

Given the graph of y=f(x), shown as a red dashed curve, drag the movable blue point to obtain the graph of y=f(x−4)+3.

Answer 1

The graph of the function f(x),which is in the shape of parabola has vertex at (0,0).

→y=x²

f(x)=x²

Now, the graph of f(x) is translated by 2 units in horizontally right Direction.

→ y=(x-2)²

f(x-2)=(x-2)²

Now, we have to obtain the graph of the function

→y=f(x-4)+3

y=(x-4)²+3

The function , f(x-2) is shifted , 2 unit right in Horizontal right direction and, 3 unit up in vertically Upward direction.

Answer 2

See graph in attachment.

Explanation:

The graph of
`y=f(x)` is a parabola that has its vertex at the origin.

The equation of the transformed graph is

`y=f(x-4)+3`

The vertex of this transformed function is

`(4,3)`

Drag the blue graph up so that the vertex will now be at (4,3).

See graph in attachment.