Do piecewise functions have parent functions?

Parent functions and transformations?

• Could someone check these for me? To see if i'm right? 1. g(x)= x squared-1 Transformation: g(x)= (x- h)squared -1 2. f(x)= 2 | x- 1| Transformation: f(x)= 2|x- 1| + k 3. H(x)= square root x- 2 Transformation: h(x)= square root x- 2 + k 4. g(x)= x cubed + 3 Transformation: (x+3)cubed +k 5. g(x)= 1/x+6 Transformation: g(x)= 1/x+6 + k 6. f(x)= |x + 5| -2 Transformation: f(x)= |x + 5| - 2 7. h(x)= 1/x - 5 Transformation: 1/x-h - 5 Parent functions: 1. Quadratic 2. Absolute Value 3. Square Root 4. Cubic 5. Reciprocal 6. Absolute Value 7. Reciprocal

• Answer:

  1/ from f(x) = x^2 , translate -1 in y direction to get g(x) 2/ from h(x) = |x| , dilate factor 2 from x-axis and translate 1 in x-direction to get f(x)