Let the graph of g be a horizontal shrink by a factor of 1/2, followed by a translation 3 units down of the graph of f(x)=|x|. Write a rule for g.

Answer 1

Which axis is horizontal: x or y?

ANSWER: X

The horizontal shrink means you shrink x by a factor of 1/2. Currently the slope on the right side of the V is 1, so to "shrink" it, you actually DIVIDE by 1/2, giving you a new slope of 2. So now our function is y=|2x|.

Which axis goes "up and down": x or y?

ANSWER: Y

The translation of 3 units down means you subtract 3 from all y values, or y-3. If f(x)=y, then what you get is f(x) - 3 = |x| - 3.

Put it all together:

g(x) = |2x| - 3