Transformations of Functions

Topic:
Functions

g(x)=f(x)+k

g(x)=f(x)+k

How is the parent function f(x) transformed by adding k? Be sure to discusses the case where k is positive and k is negative.

g(x)=f(x-h)

g(x)=f(x-h)

How is the parent function f(x) transformed by subtracting h DIRECTLY from x? Be sure to discusses the case where h is positive and h is negative.

g(x)=af(x)

g(x)=af(x)

How is the parent function f(x) transformed by multiplying by a? Be sure to discusses the case where a is positive and a is negative.

g(x)=f(cx)

g(x)=f(cx)

How is the parent function f(x) transformed by multiplying x DIRECTLY by c? Be sure to discusses the cases where c is positive/negative and |c|>1 or |c|<1.