Question

given the function f(x)=x^2-6x+5, show all work necessary to draw the graph of g(x)=f(|2x|-3)

Answer 1

step 1
http://www.wolframalpha.com/input/?i=y%3Dx^2-6x%2B5 the graph of the
function
step 2
http://www.wolframalpha.com/input/?i=y%3Dx^2-6x%2B5
taking the absolute value means what you see to the right side of the y - axis you see on the left.
step 3
http://www.wolframalpha.com/input/?i=y%3D |%282x%29^2|-6|2x|%2B5
doubling x makes everything steeper.
step 4
http://www.wolframalpha.com/input/?i=y%3D |%282x-3%29^2|-6|2x-3|%2B5
shifts to the right 3 units