Question

Suppose F (X)=x2. Find the graPh of. f(x+4)

Answer 1

Graph of f(x+4) has been shown in the attached file.

Explanation:

We have been given that
`f(x)=x^2`

On substituting x = x+4, we get

`f(x)=(x+4)^2`

Now, we know that the parent function
`f(x)=x^2` represents a parabola whose vertex is at (0,0).

When we add any constant c in x then the parent function shifts c units left.

Since, we have added 4 in x, hence the graph of the given function will shift 4 units left. Thus, the vertex of the new parabola will be (-4,0)

Graph of f(x+4) has been shown in the attached file.