18.5k views
2 votes
Suppose f(x)=x^2.Find the graph of f(x+3)

2 Answers

1 vote
Replace x with x+3:
f(x+3) = (x+3)²
which is x² translated 3 units left
User Lasitha Lakmal
by
8.2k points
3 votes

Answer with explanation:

We are given a parent function f(x) by:


f(x)=x^2

i.e. the graph of the function f(x) is a parabola with vertex at (0,0)

Also, we know that the transformation of the type:

f(x) → f(x+k)

is a shift or the translation of the function f(x) k units to the left or to the right depending on k.

if k>0 then the shift is k units to the left.

and if k<0 then the shift is k units to the right.

Here we have to graph the function:

f(x+3) i.e. k=3>0 i.e. the graph of this function is the shift of the graph of the function f(x) 3 units to the left.

i.e. the graph of f(x+3) is a upward open parabola with vertex at (-3,0).

i.e.
f(x)=(x+3)^2

Suppose f(x)=x^2.Find the graph of f(x+3)-example-1
User Bing
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories