The graph of a function y fx is pictured with domain 1 x 1

The graph of a function y = f(x) is pictured with domain -1 x 1. Sketch the graph of the new function y = g(x) = 1/pi f(3x) - 0.5. Find the larges possible domain of the function y = g(x). -infinity x infinity -1/3 x 1/3 -1/3 x 0 0 x 1/3 -2/3 x 0

Solution

1) f(x) is given

Now we have : g(x) = (1/n)f(3x) -0.5

Following steps to get the graph of g(x) from f(x)

1. compressed horizontally by a factor 3 units

f(3x)

2. A vertical compression is the squeezing of the graph towards the x-axis by n units

f(3x)/n

3. 0.5 units, the graph translates (slides)downward.

Option A is the right option

2)

Domain of f(x) : -1 <= x<=1

Domain g(x) with f(3x) would be -1/3 <= x<=1/3