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 translation 1 unit down of the graph of f(x) = x ^ 2 . Write a rule for g.
Accepted Solution
A:
Answer: [tex]g(x)=-(\frac{1}{2}x)^2-1[/tex]Step-by-step explanation: Some transformations for a function f(x) are: - If [tex]f(x)-k[/tex], the function is shifted down "k" units. - If [tex]y= f(bx)[/tex] and [tex]0<b<1[/tex], the function is horizontally shrunk (or compressed). - If [tex]-f(x)[/tex], the function is reflected over the x-axis. Therefore, knowing these transformations for a function, and knowing that the transformation the function g(x) is obtained by: - Shrinking horizontally the function f(x) by a factor of [tex]\frac{1}{2}[/tex]. - Reflecting the function f(x) in the x-axis. - Translating the function f(x) 1 units down. You can write the following function: [tex]g(x)=-(\frac{1}{2}x)^2-1[/tex]