Algebra homework

Question

let the graph of g be a horizontal shrink by a factor of 1/2 and a reflection in the x axis, followed by a transition 1 unit down of the graph of f (x)=x2 write a rule for g

Answer 1

Let's go step by step. I presume rhe function is f(x)=x².

Horizontal shrink by a factor of 1/2. Transformations inside the parentheses affect the horizontal, and they operate opposite of the way we normally expect.

So, this is g(x) = (2x)²

Next, let's reflect across the x-axis:

g(x) = - (2x)²

Finally, let's transition (shift) the graph one unit down:

g(x) = - (2x)² -1

Since both the reflection and the shift down are vertical operations, they are controlled by operators outside the parentheses. Also, they are carried out in an intuitively logical manner.

You could also write this as g(x) = - f(2x) -1.