Algebra 120 on transformations

Question

Describe the transformations that would produce the graph of g from the graph of f. Be specific and detailed. If more than one transformation is needed, specify the transformation that should be applied.

a. g(x)=f(2x)+4

b. g(x)= -f(x-4)-9

Answer 1

The general rules of transformations are a f(b(x+h)) + k

k - vertical shift up/down

h - horizontal shift down/up (the opposite) - So positive h=3 means a horizontal shift left (negative) 3 spaces.

a - vertical stretch/shrink. Negative a is reflection over x-axis.

b - horizontal shrink/stretch (the opposite) - So b=3 is a horizontal shrink of 1/3. Negative b is reflection over y-axis. Also, note the parentheses b(x+h), b distributes to both the x and the h.

So, for your problems:

a. g(x) = f(2x)+4 is a horizontal shrink by 1/2 and upward shift 4 units

b. g(x)= -f(x-4)-9 is a rightward shift 4 units, downward shift 9 units and reflection over x-axis.