Question

Transformation function. Please help.

Answer 1

so this time would you do 2x-1(-x^2+1) ?

Answer 2

f(x) = -x^2 + 1
There are a few things you can conclude about this function:
It is a parabola. It is an inverted parabola because of the negative coefficient (-1) of the x^2 term. When x = 0, y = 1.
So an inverted parabola that has a y-intercept of +1. This itself lets you pick the correct answer straight away.

But let us do g(x) for the sake of completeness...

Answer 3

f(x) = -x^2 + 1
g(x) = f(2x) - 1
= -(2x)^2 +1 - 1
= -4x^2
g(x) = -4x^2.
This is also an inverted parabola. When x = 0, y = 0. So the parabola has a y-intercept of 0.

Two inverted parabolas, one with a y-intercept of +1 and another with a y-intercept of 0.

Answer 4

so then it would be B because it is the only one that fits a parabola

Answer 5

Yes, it is B.

If f(x) = -x^2 + 1
and you are asked to find f(3) you will simply replace x by 3.
f(3) = -(3)^2 + 1 = -9 + 1 = -8

Similarly, if f(x) = -x^2 + 1 and you are asked to find f(2x), replace x by 2x:
f(2x) = -(2x)^2 + 1 = -4x^2 + 1
g(x) = f(2x) - 1 = -4x^2 + 1 - 1 = -4x^2

Answer 6

Thank you again. You are very helpful with explaining haha

Answer 7

You are welcome. Glad to be able to help.