1. ## f(x) problem

The question is

Let f(x)= x². Evaluate g(x)= -2f(x+1) + 1 and plot each transformation in steps, the last graph should be the graph of g.

2. Originally Posted by romanianxromo
The question is

Let f(x)= x². Evaluate g(x)= -2f(x+1) + 1 and plot each transformation in steps, the last graph should be the graph of g.
Okay let's see...

If $f(x) = x^2$ then obviously $f(x + 1) = (x + 1)^2$

So then:

$g(x) = -2(x+1)^2 + 1$

Will you be able to draw it now?

3. Originally Posted by romanianxromo
The question is

Let f(x)= x². Evaluate g(x)= -2f(x+1) + 1 and plot each transformation in steps, the last graph should be the graph of g.
1) $f(x+1) = (x+1)^2$ parabola centered at -1 facing up.

2) $-2f(x+1) = -2(x+1)^2$ parabola centered at -1 facing down and amplified by 2.

3) $-2f(x+1) + 1 = -2(x+1)^2 + 1$ parabola centered at -1 facing down and amplified by 2, which is then shifted up along y-axis by 1 unit.

4. Originally Posted by Isomorphism
1) $f(x+1) = (x+1)^2$ parabola centered at -1 facing up.

2) $-2f(x+1) = -2(x+1)^2$ parabola centered at -1 facing down and amplified by 2.

3) $-2f(x+1) + 1 = -2(x+1)^2 + 1$ parabola centered at -1 facing down and amplified by 2, which is then shifted up along y-axis by 1 unit.
Thank you! This was very helpful!